Log in

Relevant bibliographies by topics / Biharmonic equation / Journal articles

To see the other types of publications on this topic, follow the link: Biharmonic equation.

Journal articles on the topic 'Biharmonic equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 25 July 2025

Create a spot-on reference in APA, MLA, Chicago, Harvard, and other styles

Select a source type:

Consult the top 50 journal articles for your research on the topic 'Biharmonic equation.'

Next to every source in the list of references, there is an 'Add to bibliography' button. Press on it, and we will generate automatically the bibliographic reference to the chosen work in the citation style you need: APA, MLA, Harvard, Chicago, Vancouver, etc.

You can also download the full text of the academic publication as pdf and read online its abstract whenever available in the metadata.

Browse journal articles on a wide variety of disciplines and organise your bibliography correctly.

1

Li, Jin. "Linear barycentric rational collocation method for solving biharmonic equation." Demonstratio Mathematica 55, no. 1 (2022): 587–603. http://dx.doi.org/10.1515/dema-2022-0151.

Full text

Abstract:

Abstract Two-dimensional biharmonic boundary-value problems are considered by the linear barycentric rational collocation method, and the unknown function is approximated by the barycentric rational polynomial. With the help of matrix form, the linear equations of the discrete biharmonic equation are changed into a matrix equation. From the convergence rate of barycentric rational polynomial, we present the convergence rate of linear barycentric rational collocation method for biharmonic equation. Finally, several numerical examples are provided to validate the theoretical analysis.

APA, Harvard, Vancouver, ISO, and other styles

2

GARNADI, A. D. "MIXED FINITE ELEMENT FORMULATION OF THE BIHARMONIC EQUATION." Journal of Mathematics and Its Applications 4, no. 1 (2005): 1. http://dx.doi.org/10.29244/jmap.4.1.1-12.

Full text

Abstract:

<p>We will provide an abstract setting for mixed ﬁnite element method for biharmonic equation. The abstract setting casts mixed ﬁnite element method for ﬁrst biharmonic equation and sec- ond biharmonic equation into a single framework altogether. We provide error estimates for both type biharmonic equation, and for the ﬁrst time an error estimate for the second biharmonic equation.</p>

APA, Harvard, Vancouver, ISO, and other styles

3

Vaskevich, V. L. "SPHERICAL SPLINE SOLUTIONS OF THE INHOMOGENEOUS BIHARMONIC EQUATION." Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki 64, no. 8 (2024): 1456–65. https://doi.org/10.31857/s0044466924080107.

Full text

Abstract:

An inhomogeneous biharmonic equation is considered on the unit sphere in three-dimensional space. The solution of this equation, belonging to the Sobolev space on the sphere, is approximated by a sequence of solutions of the same equation but with specific right-hand sides, represented as linear combinations of shifts of the Dirac delta function. It is proven that, given specified nodes on the sphere determining the shifts, special solutions of the equation — spherical biharmonic splines — exist, and the weights corresponding to each are solutions of an associated non-degenerate system of line

APA, Harvard, Vancouver, ISO, and other styles

4

ZHAI, SHUYING, XINLONG FENG, and YINNIAN HE. "A ROBUST HIGH-ORDER COMPACT METHOD FOR THE THREE DIMENSIONAL NONLINEAR BIHARMONIC EQUATIONS." International Journal of Computational Methods 11, no. 04 (2014): 1350065. http://dx.doi.org/10.1142/s0219876213500655.

Full text

Abstract:

In this paper, a new family of fourth-order compact finite difference schemes are considered using coupled approach for numerical solutions of the three-dimensional (3D) linear biharmonic problems. A new fourth-order accurate algorithm is developed through the different composition of these schemes for 3D nonlinear biharmonic equations. And an optimal combination is found in numerical experiments. The main advantage of this algorithm is that it avoids the difficulties of constructing high order compact difference schemes for 3D nonlinear biharmonic equations. The numerical solutions of unknown

APA, Harvard, Vancouver, ISO, and other styles

5

Sundaravadivel, Priyadharshini, Sadhasivam Vadivel, Viswanathan Kodakkal Kannan, and Sankar Duraisamy Sambasivam. "Picone Identities of a Certain Class of Conformable Half Linear Anisotropic Biharmonic Equations." Malaysian Journal of Fundamental and Applied Sciences 21, no. 1 (2025): 1719–25. https://doi.org/10.11113/mjfas.v21n1.3549.

Full text

Abstract:

Main aim of this article, we derive sufficient conditions of new results for Picone identities for a certain class of conformable half-linear anisotropic biharmonic equations. We derive a Strumiancomparison theorem and oscillation results. Furthermore, the oscillation results are different from the most known ones in the sense that they are based on the information for radial solutions. This paper's expand upon and broaden a few of the previously established results for conformable half-linear anisotropic biharmonic equations. If and then conformable half-linear anisotropic biharmonic equation

APA, Harvard, Vancouver, ISO, and other styles

6

Kononov, Yuriy. "On the solution of a complicated biharmonic equation in a hydroelasticity problem." Ukrainian Mathematical Bulletin 20, no. 2 (2023): 203–18. http://dx.doi.org/10.37069/1810-3200-2023-20-2-3.

Full text

Abstract:

A hydroelastic problem of free vibrations of a thin plate that horizontally separates ideal incompressible liquids of different densities in a rigid cylindrical tank with an arbitrary cross-section has been considered in the linear formulation. To solve the corresponding complicated inhomogeneous biharmonic equation, the fundamental system of the solutions of biharmonic equation (FSS) and the eigenmodes of ideal liquid oscillations in a cylindrical cavity were used. The frequency equation was obtained for arbitrary fixation of the plate contour. On the example of a clamped plate, the frequency

APA, Harvard, Vancouver, ISO, and other styles

7

Qian, Xiaoyong, Jun Wang, and Maochun Zhu. "Multiple Nontrivial Solutions for a Class of Biharmonic Elliptic Equations with Sobolev Critical Exponent." Mathematical Problems in Engineering 2018 (November 21, 2018): 1–12. http://dx.doi.org/10.1155/2018/8212785.

Full text

Abstract:

In this paper, we study the existence and multiplicity of nontrivial solutions for a class of biharmonic elliptic equation with Sobolev critical exponent in a bounded domain. By using the idea of the previous paper, we generalize the results and prove the existence and multiplicity of nontrivial solutions of the biharmonic elliptic equations.

APA, Harvard, Vancouver, ISO, and other styles

8

Algazin, O., and A. Kopaev. "Exact solutions of the Navier boundary value problem for a biharmonic equation with a special right-hand side in an infinite layer." Bulletin of State University of Education. Series: Physics and Mathematics, no. 3 (January 27, 2024): 6–14. https://doi.org/10.18384/2949-5067-2023-3-6-14.

Full text

Abstract:

Aim. Purpose is to find exact solutions of the boundary value problem for the biharmonic equation in an infinite 𝑛𝑛-dimensional layer with Navier boundary conditions. Methodology. The paper considers a boundary value problem for a biharmonic equation in an infinite n-dimensional layer. The paper considers a boundary value problem for a biharmonic equation in an infinite n-dimensional layer 𝑥 ∈ Rn, 0 < y < a with Navier boundary conditions. This problem reduces to the sequential solution of two Dirichlet problems for the Poisson equation, the explicit solutions of which were obtained earl

APA, Harvard, Vancouver, ISO, and other styles

9

Grunau, Hans-Christoph, Nobuhito Miyake, and Shinya Okabe. "Positivity of solutions to the Cauchy problem for linear and semilinear biharmonic heat equations." Advances in Nonlinear Analysis 10, no. 1 (2020): 353–70. http://dx.doi.org/10.1515/anona-2020-0138.

Full text

Abstract:

Abstract This paper is concerned with the positivity of solutions to the Cauchy problem for linear and nonlinear parabolic equations with the biharmonic operator as fourth order elliptic principal part. Generally, Cauchy problems for parabolic equations of fourth order have no positivity preserving property due to the change of sign of the fundamental solution. One has eventual local positivity for positive initial data, but on short time scales, one will in general have also regions of negativity. The first goal of this paper is to find sufficient conditions on initial data which ensure the e

APA, Harvard, Vancouver, ISO, and other styles

10

Turmetov, B. Kh, and V. V. Karachik. "NEUMANN BOUNDARY CONDITION FOR A NONLOCAL BIHARMONIC EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 14, no. 2 (2022): 51–58. http://dx.doi.org/10.14529/mmph220205.

Full text

Abstract:

The solvability conditions for a class of boundary value problems for a nonlocal biharmonic equation in the unit ball with the Neumann conditions on the boundary are studied. The nonlocality of the equation is generated by some orthogonal matrix. The presence and uniqueness of a solution to the proposed Neumann boundary condition is examined, and an integral representation of the solution to the Dirichlet problem in terms of the Green's function for the biharmonic equation in the unit ball is obtained. First, some auxiliary statements are established: the Green's function of the Dirichlet prob

APA, Harvard, Vancouver, ISO, and other styles

11

Wang, Xue Hai, Ya Mei Liu, and Qi Xun Lan. "A Hybrid Radial Boundary Node Method for Biharmonic Problems." Advanced Materials Research 243-249 (May 2011): 6003–6. http://dx.doi.org/10.4028/www.scientific.net/amr.243-249.6003.

Full text

Abstract:

The hybrid radial boundary node method is applied to solve the biharmonic problems. Based on modified variational principle, the variational formula of the biharmonic problems is established. The radial basis point interpolation is employed to approximate the boundary variables, while the domain variables are interpolated by a combination of the fundamental solution of the laplace equation and the biharmonic equation. Compared to the regular hybrid boundary node method, as the shape function has the delta function property, the boundary conditions of the original problem can be easily implemen

APA, Harvard, Vancouver, ISO, and other styles

12

Gao, Lin, Zhizhen Zhang, and Yan Xing. "Analytical solutions of biharmonic equation by the Fourier-Yang integral transform." Thermal Science 23, Suppl. 3 (2019): 765–71. http://dx.doi.org/10.2298/tsci180510091g.

Full text

Abstract:

The biharmonic equation are frequently encountered in CFD. In this investigation, the biharmonic equation in the semi-infinite domains is addressed using a new Fourier-like integral transform proposed in [1]. The properties of the new Fourier-like integral transform are expanded in this article. Meanwhile, the analytical solutions for the biharmonic equation in the semi-infinite domains are found. This demonstrates the new Fourier-like integral transform is an efficient and accurate method to clarify mathematical physics problems described by PDE.

APA, Harvard, Vancouver, ISO, and other styles

13

Ghergu, Marius. "A biharmonic equation with singular nonlinearity." Proceedings of the Edinburgh Mathematical Society 55, no. 1 (2011): 155–66. http://dx.doi.org/10.1017/s0013091510000234.

Full text

Abstract:

AbstractWe study the biharmonic equation Δ2u=u−α, 0 < α < 1, in a smooth and bounded domain Ω ⊂ ℝn,n≥ 2, subject to Dirichlet boundary conditions. Under some suitable assumptions on Ω related to the positivity of the Green function for the biharmonic operator, we prove the existence and uniqueness of a solution.

APA, Harvard, Vancouver, ISO, and other styles

14

Doss, L. Jones Tarcius, N. Kousalya, and S. Sundar. "A Finite Pointset Method for Biharmonic Equation Based on Mixed Formulation." International Journal of Computational Methods 15, no. 07 (2018): 1850068. http://dx.doi.org/10.1142/s0219876218500688.

Full text

Abstract:

In this paper, a meshless method based on finite point set is presented for solving the biharmonic equation with simply supported boundary condition. The biharmonic equation is split into a coupled system of two Poisson equations by introducing an intermediate function. The system of two Poisson equations is then solved by finite pointset method. This method is a local iterative method based on the weighted least square approximation. The advantage of this method is that two resultant of sizes only [Formula: see text] matrices are solved at each particle for the original and intermediate solut

APA, Harvard, Vancouver, ISO, and other styles

15

Masood, Y., A. H. Kara, and F. D. Zaman. "An Invariance and Closed Form Analysis of the Nonlinear Biharmonic Beam Equation." Malaysian Journal of Mathematical Sciences 17, no. 2 (2023): 211–25. http://dx.doi.org/10.47836/mjms.17.2.09.

Full text

Abstract:

In this paper, we study the one-parameter Lie groups of point transformations that leave invariant the biharmonic partial differential equation (PDE) uxxxx+2uxxyy+uyyyy=f(u) . To this end, we construct the Lie and Noether symmetry generators and present reductions of biharmonic PDE. When f is arbitrary function of u, we obtain the solution of biharmonic equation in terms of Green function. The equation is further analysed when f is exponential function and for general power law. Furthermore, we use Noether's theorem and the 'multiplier approach' to construct conservation laws of the PDE.

APA, Harvard, Vancouver, ISO, and other styles

16

Wang, Huanhuan. "Mixed Direct Discontinuous Galerkin Method for the Biharmonic Equation." Journal of Physics: Conference Series 2660, no. 1 (2023): 012028. http://dx.doi.org/10.1088/1742-6596/2660/1/012028.

Full text

Abstract:

Abstract In this paper, we use the mixed direct discontinuous Galerkin method (DDG) to solve the biharmonic equation. Firstly, by introducing an auxiliary variable, the biharmonic equation is split into two second-order equations. Secondly, the variational problem based on the DDG method of the system is derived and its well-posedness is proven. Next, error estimates of the approximate solution in L 2 norm and energy norm are present. For a given polynomial degree k (k ≥ 1), the optimal convergence rates concerning energy norm and norm are k and k + 1, respectively. Finally, numerical results

APA, Harvard, Vancouver, ISO, and other styles

17

Sabo, Sadiq Shehu, Umar Muhammad Dauda, Sunday Babuba, and Abba Ibrahim Bakari. "ON NONLINEAR BIHARMONIC DISPERSIVE WAVE EQUATIONS." FUDMA JOURNAL OF SCIENCES 9, no. 1 (2025): 87–100. https://doi.org/10.33003/fjs-2025-0901-2925.

Full text

Abstract:

This paper proposes and studies particular nonlinear dispersive biharmonic equation, whose related equations appear in various physical phenomena such as wave propagation in nonlinear media and plasma physics. We chose the power kind of nonlinearity as it is common in these areas. We show that the linear version exhibits strong dispersive behaviour while the nonlinear version reveals possible emergence of singularities for higher degree nonlinearity exponent . Both versions of the equation, linear and nonlinear, were solved analytically where for the latter we use perturbation approach and Fou

APA, Harvard, Vancouver, ISO, and other styles

18

Dunninger, D. R., and M. Miklavčič. "On a semilinear biharmonic equation." Nonlinear Analysis: Theory, Methods & Applications 16, no. 4 (1991): 383–87. http://dx.doi.org/10.1016/0362-546x(91)90037-2.

Full text

APA, Harvard, Vancouver, ISO, and other styles

19

Arias, Eduardo, Marco Calahorrano, and Alfonso Castro. "biharmonic equation with discontinuous nonlinearities." Electronic Journal of Differential Equations 2024, no. 01-?? (2024): 15. http://dx.doi.org/10.58997/ejde.2024.15.

Full text

Abstract:

We study the biharmonic equation with discontinuous nonlinearity and homogeneous Dirichlet type boundary conditions $$\displaylines{ \Delta^2u=H(u-a)q(u) \quad \hbox{in }\Omega,\cr u=0 \quad \hbox{on }\partial\Omega,\cr \frac{\partial u}{\partial n}=0 \quad \hbox{on }\partial\Omega, }$$ where \(\Delta\) is the Laplace operator, \(a> 0\), \(H\) denotes the Heaviside function, \(q\) is a continuous function, and \(\Omega\) is a domain in \(R^N \) with \(N\geq 3\). Adapting the method introduced by Ambrosetti and Badiale (The Dual Variational Principle), which is a modification of Clarke and E

APA, Harvard, Vancouver, ISO, and other styles

20

Galanin, Mikhail, Daniel Milyutin, and Evgeny Savenkov. "FINITE SUPERELEMENTS METHOD FOR BIHARMONIC EQUATION." Mathematical Modelling and Analysis 12, no. 3 (2007): 309–24. http://dx.doi.org/10.3846/1392-6292.2007.12.309-324.

Full text

Abstract:

In this work finite superelements method (FSEM) for solution of biharmonic equation in bounded domains is proposed and developed. The method is based on decomposition of domain into subdomains with the solution of a number of intermediary problems, every of which is a boundary value problem for biharmonic equation with boundary condition being basis for interpolation of solution at superelements boundaries. The initial problem solution is found as an expansion on the constructed function system. It is shown that the solution of general problem can be recovered using functions and traces found

APA, Harvard, Vancouver, ISO, and other styles

21

Can, Nguyen, Le Long, Ho Binh, and Nguyen Luc. "Biharmonic heat equation with gradient non-linearity on Lp space." Thermal Science 25, Spec. issue 2 (2021): 359–65. http://dx.doi.org/10.2298/tsci21s2359c.

Full text

Abstract:

In this paper, we deal with the biharmonic heat equation with gradient non-linearity. Under the suitable condition of the initial datum, we show that the global unique existence of the mild solution. The main technique in the paper is to use Banach?s fixed point theorem in combination with the Lp-Lq evaluation of biharmonic operator.

APA, Harvard, Vancouver, ISO, and other styles

22

Körpınar, Talat, and Essin Turhan. "Darboux rotation axis of spacelike biharmonic helices with timelike normal in the Lorentzian E(1, 1)." Boletim da Sociedade Paranaense de Matemática 31, no. 1 (2011): 9. http://dx.doi.org/10.5269/bspm.v31i1.14872.

Full text

Abstract:

In this paper, we study Darboux rotation axis for spacelike biharmonic helices in the Lorentzian group of rigid motions E(1,1). We obtain equation of Darboux vector of spacelike biharmonic helices in the Lorentzian E(1,1).

APA, Harvard, Vancouver, ISO, and other styles

23

GARNADI, A. D. "ON THE USE OF DISCRETE FOURIER TRANSFORM FOR SOLVING BIPERIODIC BOUNDARY VALUE PROBLEM OF BIHARMONIC EQUATION IN THE UNIT RECTANGLE." Journal of Mathematics and Its Applications 2, no. 2 (2003): 37. http://dx.doi.org/10.29244/jmap.2.2.37-42.

Full text

Abstract:

This note is addressed to solving biperiodic boundary value problem of biharmonic equation in the unit rectangle. First, we describe the necessary tools, which is discrete Fourier trans- form for one dimensional periodic sequence, and then extended the results to 2-dimensional biperiodic sequence. Next, we use the discrete Fourier transform 2-dimensional biperiodic sequence to solve discretization of the biperiodic boundary value problem of Biharmonic Equation.

APA, Harvard, Vancouver, ISO, and other styles

24

Hamydy, Ahmed, Mohamed Massar, and Hilal Essaouini. "Existence of solutions for a biharmonic equation with gradient term." Studia Universitatis Babes-Bolyai Matematica 68, no. 4 (2023): 873–84. http://dx.doi.org/10.24193/subbmath.2023.4.14.

Full text

Abstract:

"In this paper, we mainly study the existence of radial solutions for a class of biharmonic equation with a convection term, involving two real parameters λ and ρ. We mainly use a combination of the fixed-point index theory and the Banach contraction theorem to prove that there are λ0 > 0 and ρ0 > 0 such the equation admits at least one radial solution for all (λ, ρ) ∈ [−λ0, ∞[ × [0, ρ0]. Keywords: Radial solution, biharmonic equation, index theory, existence."

APA, Harvard, Vancouver, ISO, and other styles

25

Liu, Xianwei, Huacong Li, Xinxing Shi, and Jiangfeng Fu. "Application of biharmonic equation in impeller profile optimization design of an aero-centrifugal pump." Engineering Computations 36, no. 5 (2019): 1764–95. http://dx.doi.org/10.1108/ec-08-2018-0378.

Full text

Abstract:

Purpose The purpose of this paper is to improve the hydraulic efficiency without changing the overall dimension. The blade profile optimization design of the aero-centrifugal pump based on the biharmonic equation surrogate model has been studied. Design/methodology/approach First of all, Bezier curves and linear function are used to control the annular angle distribution and the stacking angle of blade profile under the MATLAB platform. Grid independence analysis has been studied to find the finest mesh scheme. After the precision comparison of test data and computation fluid dynamics 15 sets

APA, Harvard, Vancouver, ISO, and other styles

26

Shivanian, Elyas. "A Meshless Method Based on Radial Basis and Spline Interpolation for 2-D and 3-D Inhomogeneous Biharmonic BVPs." Zeitschrift für Naturforschung A 70, no. 8 (2015): 673–82. http://dx.doi.org/10.1515/zna-2015-0100.

Full text

Abstract:

AbstractThis paper presents a meshless method which, at the first step, utilises the radial basis functions collocation scheme to approximate the unknown function at specific nodal points. The difficulty of these biharmonic-type problems is the multiple boundary conditions, as well as high derivatives terms. The inhomogeneous biharmonic equation is replaced by two Poisson equations of an intermediate function where Neumann’s boundary conditions is of second derivatives. It uses the imposed-kernel technique (IKT) to overcome multiple boundary conditions where Neumann’s boundary conditions is of

APA, Harvard, Vancouver, ISO, and other styles

27

Perktaş, Selcen, Erol Kiliç, and Sadik Keleş. "Biharmonic Hypersurfaces of LP-Sasakian Manifolds." Annals of the Alexandru Ioan Cuza University - Mathematics 57, no. 2 (2011): 387–408. http://dx.doi.org/10.2478/v10157-011-0034-z.

Full text

Abstract:

Biharmonic Hypersurfaces of LP-Sasakian Manifolds In this paper the biharmonic hypersurfaces of Lorentzian para-Sasakian manifolds are studied. We firstly find the biharmonic equation for a hypersurface which admits the characteristic vector field of the Lorentzian para-Sasakian as the normal vector field. We show that a biharmonic spacelike hypersurface of a Lorentzian para-Sasakian manifold with constant mean curvature is minimal. The biharmonicity condition for a hypersurface of a Lorentzian para-Sasakian manifold is investigated when the characteristic vector field belongs to the tangent h

APA, Harvard, Vancouver, ISO, and other styles

28

Turmetov, Batirkhan, Valery Karachik, and Moldir Muratbekova. "On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions." Mathematics 9, no. 17 (2021): 2020. http://dx.doi.org/10.3390/math9172020.

Full text

Abstract:

A nonlocal analogue of the biharmonic operator with involution-type transformations was considered. For the corresponding biharmonic equation with involution, we investigated the solvability of boundary value problems with a fractional-order boundary operator having a derivative of the Hadamard-type. First, transformations of the involution type were considered. The properties of the matrices of these transformations were investigated. As applications of the considered transformations, the questions about the solvability of a boundary value problem for a nonlocal biharmonic equation were studi

APA, Harvard, Vancouver, ISO, and other styles

29

Bluman, George W., and R. Douglas Gregory. "On transformations of the biharmonic equation." Mathematika 32, no. 1 (1985): 118–30. http://dx.doi.org/10.1112/s0025579300010937.

Full text

APA, Harvard, Vancouver, ISO, and other styles

30

Wang, Dong. "Concentration for a biharmonic Schrödinger equation." Pacific Journal of Mathematics 289, no. 2 (2017): 469–87. http://dx.doi.org/10.2140/pjm.2017.289.469.

Full text

APA, Harvard, Vancouver, ISO, and other styles

31

Ramm, A. G. "An inverse problem for biharmonic equation." International Journal of Mathematics and Mathematical Sciences 11, no. 2 (1988): 413–15. http://dx.doi.org/10.1155/s0161171288000493.

Full text

APA, Harvard, Vancouver, ISO, and other styles

32

Díaz, Martín, and Ismael Herrera. "TH-collocation for the biharmonic equation." Advances in Engineering Software 36, no. 4 (2005): 243–51. http://dx.doi.org/10.1016/j.advengsoft.2004.10.007.

Full text

APA, Harvard, Vancouver, ISO, and other styles

33

Xu, Shao Peng, and Shu Lin Zhou. "Zero Extension for the Biharmonic Equation." Acta Mathematica Sinica, English Series 34, no. 10 (2018): 1549–62. http://dx.doi.org/10.1007/s10114-018-7328-y.

Full text

APA, Harvard, Vancouver, ISO, and other styles

34

Kaewumpai, Supanut, Suwon Tangmanee, and Anirut Luadsong. "A Meshless Local Petrov-Garlerkin Method for Solving the Biharmonic Equation." Advanced Materials Research 931-932 (May 2014): 1488–94. http://dx.doi.org/10.4028/www.scientific.net/amr.931-932.1488.

Full text

Abstract:

A meshless local Petrov-Galerkin method (MLPG) using Heaviside step function as a test function for solving the biharmonic equation with subjected to boundary of the second kind is presented in this paper. Nodal shape function is constructed by the radial point interpolation method (RPIM) which holds the Kroneckers delta property. Two-field variables local weak forms are used in order to decompose the biharmonic equation into a couple of Poisson equations as well as impose straightforward boundary of the second kind, and no special treatment techniques are required. Selected engineering numeri

APA, Harvard, Vancouver, ISO, and other styles

35

Ying Han, Ying Han, Mingduan Liang Liang, and Ding Peng Ding Peng. "A Priori Error Estimates for Biharmonic Eigenvalue Problems with Simply Supported Boundary Conditions." Journal of Research in Applied Mathematics 11, no. 4 (2025): 126–39. https://doi.org/10.35629/0743-1104126139.

Full text

Abstract:

The biharmonic eigenvalue problem is a classical fourth-order partial differential equation and a subject of significant research interest, particularly in applied fields such as elasticity, fluid mechanics, and quantum mechanics. Specifically, the biharmonic eigenvalue problem under simply supported boundary conditions finds wide applications in thin plate vibration modeling. To accurately solve such problems, numerical methods play a crucial role. Among them, the discontinuous Galerkin finite element method offers high mesh flexibility and adaptability, enabling arbitrary high-order accuracy

APA, Harvard, Vancouver, ISO, and other styles

36

MONTALDO, S., and A. RATTO. "BIHARMONIC CURVES INTO QUADRICS." Glasgow Mathematical Journal 57, no. 1 (2014): 131–41. http://dx.doi.org/10.1017/s0017089514000172.

Full text

Abstract:

AbstractWe develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves in surfaces defined by a polynomial equation: In particular, we use it to give a complete classification of biharmonic curves in real quadrics of the three-dimensional Euclidean space.

APA, Harvard, Vancouver, ISO, and other styles

37

Shodiev, Dilshod S. "On the Cauchy Problem for the Biharmonic Equation." Journal of Siberian Federal University. Mathematics & Physics 15, no. 2 (2022): 199–213. http://dx.doi.org/10.17516/1997-1397-2022-15-2-199-213.

Full text

Abstract:

The work is devoted to the study of continuation and stability estimation of the solution of the Cauchy problem for the biharmonic equation in the domain G from its known values on the smooth part of the boundary @G. The problem under consideration belongs to the problems of mathematical physics in which there is no continuous dependence of solutions on the initial data. In this work, using the Carleman function, not only the biharmonic function itself, but also its derivatives are restored from the Cauchy data on a part of the boundary of the region. The stability estimates for the solution o

APA, Harvard, Vancouver, ISO, and other styles

38

Du, Liang Liang, and Xiong Hua Wu. "Natural Boundary Integral Method for Irregular Plate Problems." Applied Mechanics and Materials 138-139 (November 2011): 693–98. http://dx.doi.org/10.4028/www.scientific.net/amm.138-139.693.

Full text

Abstract:

Natural boundary integral method is applied to deal with plate problems defined in irregular domains. We divide the solution into two parts, a particular solution for inhomogeneous biharmonic equation and the general solution for homogeneous biharmonic equation. For the former, the direct expansion method of boundary conditions is used to treat the arbitrary domains, and the processes of natural boundary integral method coupling with finite element method are omitted. Numerical experiments show that the method is very simple and of high accuracy.

APA, Harvard, Vancouver, ISO, and other styles

39

Chen, Bang-Yen. "Recent Developments in Chen’s Biharmonic Conjecture and Some Related Topics." Mathematics 13, no. 9 (2025): 1417. https://doi.org/10.3390/math13091417.

Full text

Abstract:

The study of biharmonic submanifolds in Euclidean spaces was introduced in the middle of the 1980s by the author in his program studying finite-type submanifolds. He defined biharmonic submanifolds in Euclidean spaces as submanifolds whose position vector field (x) satisfies the biharmonic equation, i.e., Δ2x=0. A well-known conjecture proposed by the author in 1991 on biharmonic submanifolds states that every biharmonic submanifold of a Euclidean space is minimal, well known today as Chen’s biharmonic conjecture. On the other hand, independently, G.-Y. Jiang investigated biharmonic maps betwe

APA, Harvard, Vancouver, ISO, and other styles

40

Koshanov, B. D., A. Baiarystanov, M. Daurenkyzy, and S. O. Turymbet. "GREEN'S FUNCTIONS OF SOME BOUNDARY VALUE PROBLEMS FOR BYHARMONIC OPERATORS AND THEIR CORRECT CONSTRICTIONS." PHYSICO-MATHEMATICAL SERIES 2, no. 336 (2021): 15–23. http://dx.doi.org/10.32014/2021.2518-1726.16.

Full text

Abstract:

In this paper, a constructive method is given for constructing the Green function of the Dirichlet problem for a biharmonic equation in a multidimensional ball. The need to study boundary value problems for elliptic equations is dictated by numerous practical applications in the theoretical study of the processes of hydrodynamics, electrostatics, mechanics, thermal conductivity, elasticity theory, and quantum physics. The distributions of the potential of the electrostatic field are described using the Poisson equation. When studying the vibrations of thin plates of small deflections, biharmon

APA, Harvard, Vancouver, ISO, and other styles

41

Şahin, Onur, Barış Erbaş, and Brent Wilson. "Approximate Formulation of the Rigid Body Motions of an Elastic Rectangle Under Sliding Boundary Conditions." Acta Mechanica et Automatica 15, no. 2 (2021): 82–90. http://dx.doi.org/10.2478/ama-2021-0012.

Full text

Abstract:

Abstract Low-frequency analysis of in-plane motion of an elastic rectangle subject to end loadings together with sliding boundary conditions is considered. A perturbation scheme is employed to analyze the dynamic response of the elastic rectangle revealing nonhomogeneous boundary-value problems for harmonic and biharmonic equations corresponding to leading and next order expansions, respectively. The solution of the biharmonic equation obtained by the separation of variables, a consequence of sliding boundary conditions, gives an asymptotic correction to the rigid body motion of the rectangle.

APA, Harvard, Vancouver, ISO, and other styles

42

Shi, Jincheng, Shuman Li, Cuntao Xiao, and Yan Liu. "Spatial behavior for the quasi-static heat conduction within the second gradient of type Ⅲ." Electronic Research Archive 32, no. 11 (2024): 6235–57. http://dx.doi.org/10.3934/era.2024290.

Full text

Abstract:

<p>This article focused on investigating the spatial behavior of the quasi-static biharmonic conduction equation within the framework of type Ⅲ of the second gradient in a two-dimensional cylindrical domain. The results of growth or decay estimates were established by using a second-order differential inequality. When the distance tends to infinity, the energy either grows exponentially or decays exponentially. The results showed that the Saint-Venant principle was also valid for the quasi-static biharmonic conduction equation.</p>

APA, Harvard, Vancouver, ISO, and other styles

43

DENG, YINBIN, and YI LI. "EXPONENTIAL DECAY OF THE SOLUTIONS FOR NONLINEAR BIHARMONIC EQUATIONS." Communications in Contemporary Mathematics 09, no. 05 (2007): 753–68. http://dx.doi.org/10.1142/s0219199707002629.

Full text

Abstract:

The purpose of this paper is to establish the exponential decay properties of the solutions for the nonlinear biharmonic equation [Formula: see text] We introduce the fundamental solutions for the linear biharmonic operator Δ2 - λ if λ < 0. By applying some properties of Hankel functions, which are the solutions of Bessel's equation, we obtain the asymptotic representation of the fundamental solution of Δ2 - λ at ∞ and 0. Asymptotic estimates of the solutions of (*) can be obtained from the properties of the fundamental solutions of Δ2 - λ.

APA, Harvard, Vancouver, ISO, and other styles

44

Pan, Wen-Wu, and Cheng-En Yu. "Existence of Multiple Solutions for a Quasilinear Biharmonic Equation." International Scholarly Research Notices 2014 (October 29, 2014): 1–9. http://dx.doi.org/10.1155/2014/370494.

Full text

APA, Harvard, Vancouver, ISO, and other styles

45

Abrunheiro, Lígia, and Margarida Camarinha. "An Intrinsic Version of the k-Harmonic Equation." Mathematics 11, no. 17 (2023): 3628. http://dx.doi.org/10.3390/math11173628.

Full text

Abstract:

The notion of k-harmonic curves is associated with the kth-order variational problem defined by the k-energy functional. The present paper gives a geometric formulation of this higher-order variational problem on a Riemannian manifold M and describes a generalized Legendre transformation defined from the kth-order tangent bundle TkM to the cotangent bundle T*Tk−1M. The intrinsic version of the Euler–Lagrange equation and the corresponding Hamiltonian equation obtained via the Legendre transformation are achieved. Geodesic and cubic polynomial interpolation is covered by this study, being explo

APA, Harvard, Vancouver, ISO, and other styles

46

Meleshko, I. N., та P. G. Lasy. "About One Variational Problem, Leading to а Biharmonic Equation, and about the Approximate Solution of the Main Boundary Value Problem for this Equation". Science & Technique 21, № 3 (2022): 236–41. http://dx.doi.org/10.21122/2227-1031-2022-21-3-236-241.

Full text

Abstract:

. Many important questions in the theory of elasticity lead to a variational problem associated with a biharmonic equation and to the corresponding boundary value problems for such an equation. The paper considers the main boundary value problem for the biharmonic equation in the unit circle. This problem leads, for example, to the study of plate deflections in the case of kinematic boundary conditions, when the displacements and their derivatives depend on the circular coordinate. The exact solution of the considered boundary value problem is known. The desired biharmonic function can be repr

APA, Harvard, Vancouver, ISO, and other styles

47

Kharkevych, Yu I., та A. M. Shutovskyi. "Approximation of functions from Hӧlder class by biharmonic Poisson integrals". Carpathian Mathematical Publications 16, № 2 (2024): 631–37. https://doi.org/10.15330/cmp.16.2.631-637.

Full text

Abstract:

The biharmonic equation in Cartesian coordinates is considered for the case of the upper half-plane. The solution of such a fourth-order partial differential equation for given boundary conditions is represented in the form of an integral of the product of the function and the delta-shaped kernel, which in this paper plays the role of an approximating aggregate. In the paper, we found an exact equality for the upper bound of the deviation of Hölder class functions from the considered biharmonic Poisson operator in the uniform metric.

APA, Harvard, Vancouver, ISO, and other styles

48

Zhu, Yuchen. "Blow-up of solutions for a time fractional biharmonic equation with exponentional nonlinear memory." Electronic Research Archive 32, no. 11 (2024): 5988–6007. http://dx.doi.org/10.3934/era.2024278.

Full text

Abstract:

<p>In the paper, we focus on the local existence and blow-up of solutions for a time fractional nonlinear equation with biharmonic operator and exponentional nonlinear memory in an Orlicz space. We first establish a $ L^p-L^q $ estimate for solution operators of a time fractional nonlinear biharmonic equation, and obtain bilinear estimates for mild solutions. Then, based on the contraction mapping principle, we establish the local existence of mild solutions. Moreover, by using the test function method, we obtain the blow-up result of solutions.</p>

APA, Harvard, Vancouver, ISO, and other styles

49

Jeon, Youngmok. "An Indirect Boundary Integral Equation Method for the Biharmonic Equation." SIAM Journal on Numerical Analysis 31, no. 2 (1994): 461–76. http://dx.doi.org/10.1137/0731025.

Full text

APA, Harvard, Vancouver, ISO, and other styles

50

Melnikov, Y. A. "Influence Functions of a Point Force for Kirchhoff Plates with Rigid Inclusions." Journal of Mechanics 20, no. 4 (2004): 249–56. http://dx.doi.org/10.1017/s1727719100003464.

Full text

Abstract:

AbstractA semi-analytic method is proposed for two problem settings for a Kirchhoff plate containing an absolutely rigid circular inclusion and undergoing a transverse point force. The settings differ by the location (within and out of inclusion) of the force application point. In both cases, the plate's stress-strain state is simulated with a boundary value problem for the biharmonic equation stated over a doubly connected region whose inner contour represents the edge of the inclusion. Boundary conditions imposed on the inner contour bring some parameters which are found via the equations of

APA, Harvard, Vancouver, ISO, and other styles

We offer discounts on all premium plans for authors whose works are included in thematic literature selections. Contact us to get a unique promo code!