Relevant bibliographies by topics / Biharmonic equation

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  1. Journal articles
  2. Dissertations / Theses
  3. Books
  4. Book chapters
  5. Conference papers
  6. Reports

Academic literature on the topic 'Biharmonic equation'

Author: Grafiati
Published: 4 June 2021
Last updated: 25 July 2025

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Journal articles on the topic "Biharmonic equation"

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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.

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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.
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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.

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<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>
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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.

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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
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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.

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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
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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.

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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
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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.

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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
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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.

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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.
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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.

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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
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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.

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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
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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.

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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
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Dissertations / Theses on the topic "Biharmonic equation"

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Monterde, J., and Hassan Ugail. "A comparative study between Biharmonic Bezier surfaces and Biharmonic extremal surfaces." ACTA Press, 2009. http://hdl.handle.net/10454/2795.

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No<br>Given a prescribed boundary of a Bezier surface we compare the Bezier surfaces generated by two different methods, i.e. the Bezier surface minimising the Biharmonic functional and the unique Bezier surface solution of the Biharmonic equation with prescribed boundary. Although often the two types of surfaces look visually the same, we show that they are indeed different. In this paper we provide a theoretical argument showing why the two types of surfaces are not always the same.
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Ugail, Hassan. "3D facial data fitting using the biharmonic equation." ACTA Press, 2006. http://hdl.handle.net/10454/2684.

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This paper discusses how a boundary-based surface fitting approach can be utilised to smoothly reconstruct a given human face where the scan data corresponding to the face is provided. In particular, the paper discusses how a solution to the Biharmonic equation can be used to set up the corresponding boundary value problem. We show how a compact explicit solution method can be utilised for efficiently solving the chosen Biharmonic equation. Thus, given the raw scan data of a 3D face, we extract a series of profile curves from the data which can then be utilised as boundary conditions to solve
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Ugail, Hassan, and A. Sourin. "Partial differential equations for function based geometry modelling within visual cyberworlds." IEEE Computer Society, 2008. http://hdl.handle.net/10454/2612.

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We propose the use of Partial Differential Equations (PDEs) for shape modelling within visual cyberworlds. PDEs, especially those that are elliptic in nature, enable surface modelling to be defined as boundary-value problems. Here we show how the PDE based on the Biharmonic equation subject to suitable boundary conditions can be used for shape modelling within visual cyberworlds. We discuss an analytic solution formulation for the Biharmonic equation which allows us to define a function based geometry whereby the resulting geometry can be visualised efficiently at arbitrary levels of sha
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Shitta, Abiola. "Modeling Swelling Instabilities in Surface Confined Hydrogels." Scholar Commons, 2010. https://scholarcommons.usf.edu/etd/1769.

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The buckling of a material subject to stress is a very common phenomenon observed in mechanics. However, the observed buckling of a surface confined hydrogel due to swelling is a unique manifestation of the buckling problem. The reason for buckling is the same in all cases; there is a certain magnitude of force that once exceeded, causes the material to deform itself into a buckling mode. Exactly what that buckling mode is as well as how much force is necessary to cause buckling depends on the material properties. Taking both a finite difference and analytical approach to the problem, it is de
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Larsson, Karl. "Finite Element Methods for Thin Structures with Applications in Solid Mechanics." Doctoral thesis, Umeå universitet, Institutionen för matematik och matematisk statistik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-79297.

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Thin and slender structures are widely occurring both in nature and in human creations. Clever geometries of thin structures can produce strong constructions while requiring a minimal amount of material. Computer modeling and analysis of thin and slender structures have their own set of problems, stemming from assumptions made when deriving the governing equations. This thesis deals with the derivation of numerical methods suitable for approximating solutions to problems on thin geometries. It consists of an introduction and four papers. In the first paper we introduce a thread model for use i
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Гонтаренко, Д. М. "Чисельне дослідження взаємодії особливостей різного типу для задачі згину пластини". Master's thesis, Сумський державний університет, 2019. http://essuir.sumdu.edu.ua/handle/123456789/73842.

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Отримано розрахунки напружено-деформованого стану тонкостінної пластинки з частково защемленим краєм і тріщиною. Проведено дослідження взаємодії особливостей які виникають в точці зміни крайових умов та у вершині тріщини.
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Nóbrega, Alannio Barbosa. "Multiplicidade de solução do tipo multi-bump para problemas elípticos." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/9250.

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Submitted by ANA KARLA PEREIRA RODRIGUES (anakarla_@hotmail.com) on 2017-08-14T11:52:04Z No. of bitstreams: 1 arquivototal.pdf: 1035035 bytes, checksum: 24db9b859fa0c32ac6b5b442ef6e12fa (MD5)<br>Made available in DSpace on 2017-08-14T11:52:04Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 1035035 bytes, checksum: 24db9b859fa0c32ac6b5b442ef6e12fa (MD5) Previous issue date: 2016-11-28<br>In this work we study the existence of multi-bump solutions to a certain class of elliptic problems involving biharmonic problems. Moreover, we apply the method developed to biharmonic for study the exis
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McHale, Kimberley Paige Perry. "Inequalities for vibration and buckling of a clamped plate /." free to MU campus, to others for purchase, 1997. http://wwwlib.umi.com/cr/mo/fullcit?p9842551.

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Sani, F. "EXPONENTIAL-TYPE INEQUALITIES IN R^N AND APPLICATIONS TO ELLIPTIC AND BIHARMONIC EQUATIONS." Doctoral thesis, Università degli Studi di Milano, 2012. http://hdl.handle.net/2434/170626.

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Adams' inequality in its original form is nothing but the Trudinger-Moser inequality for Sobolev spaces involving higher order derivatives. In this Thesis we present Adams-type inequalities for unbounded domains in R^n and some applications to existence and multiplicity results for elliptic and biharmonic problems involving nonlinearities with exponential growth.
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Pimenta, Marcos Tadeu de Oliveira. "Estudo de alguns problemas elípticos para o operador biharmônico." Universidade de São Paulo, 2011. http://www.teses.usp.br/teses/disponiveis/55/55135/tde-07062011-084414/.

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Nesse trabalho estudamos questões de existência, multiplicidade e concentração de soluções de uma classe de problemas elípticos biharmônicos. Nos três primeiros capítulos são utilizados métodos variacionais para estudar a existência, multiplicidade e comportamento assintótico das soluções fracas não-triviais de equações de Schrödinger estacionárias biharmônicas com diferentes hipóteses sobre o potencial e sobre a não-linearidade. No último capítulo, o método de decomposição em cones duais é empregado para obter a existência de três soluções (positiva, negativa e nodal) para uma equação biharmô
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Books on the topic "Biharmonic equation"

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Atakhodzhaev, M. A. Ill-posed internal boundary value problems for the biharmonic equation. VSP, 2002.

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Atakhodzhaev, M. A. Ill-posed internal boundary value problems for the biharmonic equation. VSP, 2001.

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Lurie, Sergey A. The biharmonic problem in the theory of elasticity. Gordon and Breach, 1995.

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Hong, Jiang, and United States. National Aeronautics and Space Administration., eds. Approximate polynomial preconditioning applied to biharmonic equations on vector supercomputers. National Aeronautics and Space Administration, 1987.

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Mayo, Anita. Fast parallel iterative solution of Poisson's and the biharmonic equations on irregular regions. Courant Institute of Mathematical Sciences, New York University, 1991.

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Selvadurai, A. P. S. Partial Differential Equations in Mechanics 2: The Biharmonic Equation, Poisson's Equation. Springer Berlin / Heidelberg, 2010.

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Selvadurai, A. P. S. Partial Differential Equations in Mechanics 2: The Biharmonic Equation, Poisson's Equation. Springer London, Limited, 2013.

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Atakhodzhaev, Mukarram A. Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation. de Gruyter GmbH, Walter, 2014.

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Kelmanson, M. A., and D. B. Ingham. Boundary Integral Equation Analyses of Singular, Potential, and Biharmonic Problems. Springer London, Limited, 2012.

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Atakhodzhaev, Mukarram A. Ill-Posed Internal Boundary Value Problems for the Biharmonic Equation. de Gruyter GmbH, Walter, 2002.

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Book chapters on the topic "Biharmonic equation"

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Selvadurai, A. P. S. "The biharmonic equation." In Partial Differential Equations in Mechanics 2. Springer Berlin Heidelberg, 2000. http://dx.doi.org/10.1007/978-3-662-09205-7_1.

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Musielak, Dora. "Germain and Her Biharmonic Equation." In Sophie Germain. Springer International Publishing, 2020. http://dx.doi.org/10.1007/978-3-030-38375-6_6.

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Camp, Charles V., and G. Steven Gipson. "Boundary Elements and the Biharmonic Equation." In Lecture Notes in Engineering. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/978-3-642-84701-1_1.

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Atkinson, Kendall, David Chien, and Olaf Hansen. "A Spectral Method for the Biharmonic Equation." In Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan. Springer International Publishing, 2018. http://dx.doi.org/10.1007/978-3-319-72456-0_5.

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Vajteršic, Marián. "Fast serial algorithms for solving biharmonic equation." In Algorithms for Elliptic Problems. Springer Netherlands, 1993. http://dx.doi.org/10.1007/978-94-017-0701-5_2.

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Gürlebeck, K. "On Some Applications of the Biharmonic Equation." In Clifford Algebras and Their Application in Mathematical Physics. Springer Netherlands, 1998. http://dx.doi.org/10.1007/978-94-011-5036-1_10.

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Vajteršic, Marián. "A VLSI multigrid poisson solver amenable to biharmonic equation." In Parallel Processing: CONPAR 92—VAPP V. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55895-0_499.

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Aksoy, Ümit, and A. Okay Çelebi. "Dirichlet Problem for Inhomogeneous Biharmonic Equation in Clifford Analysis." In Trends in Mathematics. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-87502-2_3.

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Tang, X. H., and Ch I. Christov. "An Operator Splitting Scheme for Biharmonic Equation with Accelerated Convergence." In Large-Scale Scientific Computing. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11666806_44.

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Diaz, J. B., and Ram Bachan Ram. "The Biharmonic Partial Differential Equation and the Method of Descent." In Functional Analysis, Holomorphy, and Approximation Theory. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072577-5.

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Conference papers on the topic "Biharmonic equation"

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Xu, GuangTao, Francisco Chinesta, Adrien Leygue, and Michel Visonneau. "PGD for Solving the Biharmonic Equation." In ASME 2012 11th Biennial Conference on Engineering Systems Design and Analysis. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/esda2012-82484.

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Biharmonic problem has been raised in many research fields, such as elasticity problem in plate geometries or the Stokes flow problem formulated by using the stream function. The fourth order partial differential equation can be solved by applying many techniques. When using finite elements C1 continuity must be assured. For this purpose Hermite interpolations constitute an appealing choice, but it imply the consideration of many degrees of freedom at each node with the consequent impact on the resulting discrete linear problem. Spectral approaches allow exponential convergence whilst a single
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He, Xibing, and Yupei Zhang. "Nonlinear biharmonic equation with Hardy-Sobolev potential." In 2017 2nd International Conference on Materials Science, Machinery and Energy Engineering (MSMEE 2017). Atlantis Press, 2017. http://dx.doi.org/10.2991/msmee-17.2017.304.

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Jenaliyev, Muvasharkhan T., Kanzharbek B. Imanberdiyev, and Karakoz A. Aimenova. "Ill-posed problem for the biharmonic equation." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893821.

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Турсунов, Фарход, Дилшод Шодиев, and Жавохир Раззаков. "On the Cauchy problem for the biharmonic equation." In International scientific conference "Ufa autumn mathematical school - 2021". Baskir State University, 2021. http://dx.doi.org/10.33184/mnkuomsh1t-2021-10-06.85.

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Turmetov, B. Kh, and V. V. Karachik. "About one boundary value problem for the biharmonic equation." In APPLICATIONS OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’16): Proceedings of the 42nd International Conference on Applications of Mathematics in Engineering and Economics. Author(s), 2016. http://dx.doi.org/10.1063/1.4968468.

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Kal’menov, Tynysbek Sh, and Ulzada A. Iskakova. "On a boundary value problem for the biharmonic equation." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930457.

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HSIAO, G. C., and W. L. WENDLAND. "A CHARACTERIZATION OF THE CALDERÓN PROJECTOR FOR THE BIHARMONIC EQUATION." In Proceedings of the 5th International ISAAC Congress. WORLD SCIENTIFIC, 2009. http://dx.doi.org/10.1142/9789812835635_0003.

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Saaban, Azizan, Ahmed Saleh Kherd, and Noraziah Haji Man. "Construction of Cubic DP Surface Based on Biharmonic Partial Differentiation Equation." In 2014 11th International Conference on Computer Graphics, Imaging and Visualization (CGIV). IEEE, 2014. http://dx.doi.org/10.1109/cgiv.2014.19.

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Lian, Xiaopeng, and Xiaoliang Cheng. "Error analysis of compact finite difference schemes for the biharmonic equation." In 2010 2nd International Conference on Information Science and Engineering (ICISE). IEEE, 2010. http://dx.doi.org/10.1109/icise.2010.5688642.

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Saaban, Azizan, Ahmad Saleh Kherd, Noraziah Haji Man, and Samsul Ariffin Abdul Karim. "Construction of cubic Ball surface based on biharmonic partial differentiation equation." In PROCEEDINGS OF THE 21ST NATIONAL SYMPOSIUM ON MATHEMATICAL SCIENCES (SKSM21): Germination of Mathematical Sciences Education and Research towards Global Sustainability. AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4887572.

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Reports on the topic "Biharmonic equation"

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Chen, Guo, Zhilin Li, and Ping Lin. A Fast Finite Difference Method for Biharmonic Equations on Irregular Domains. Defense Technical Information Center, 2004. http://dx.doi.org/10.21236/ada444064.

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