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Relevant bibliographies by topics / Polyharmonic equation

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Academic literature on the topic 'Polyharmonic equation'

Author: Grafiati

Published: 4 June 2021

Last updated: 8 June 2024

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Journal articles on the topic "Polyharmonic equation"

1

Yuan, Hong Fen, and Valery V. Karachik. "DUNKL-POISSON EQUATION AND RELATED EQUATIONS IN SUPERSPACE." Mathematical Modelling and Analysis 20, no. 6 (2015): 768–81. http://dx.doi.org/10.3846/13926292.2015.1112856.

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Abstract In this paper, we investigate the Almansi expansion for solutions of Dunkl-polyharmonic equations by the 0-normalized system for the Dunkl-Laplace operator in superspace. Moreover, applying the 0-normalized system, we construct solutions to the Dunkl-Helmholtz equation, the Dunkl-Poisson equation, and the inhomogeneous Dunkl-polyharmonic equation in superspace.

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Yuan, Hongfen, and Valery Karachik. "Dirichlet and Neumann Boundary Value Problems for Dunkl Polyharmonic Equations." Mathematics 11, no. 9 (2023): 2185. http://dx.doi.org/10.3390/math11092185.

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Dunkl operators are a family of commuting differential–difference operators associated with a finite reflection group. These operators play a key role in the area of harmonic analysis and theory of spherical functions. We study the solution of the inhomogeneous Dunkl polyharmonic equation based on the solutions of Dunkl–Possion equations. Furthermore, we construct the solutions of Dirichlet and Neumann boundary value problems for Dunkl polyharmonic equations without invoking the Green’s function.

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Karachik, V. V. "Representation of the Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball." Дифференциальные уравнения 59, no. 8 (2023): 1057–69. http://dx.doi.org/10.31857/s0374064123080058.

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We define the elementary solution of the polyharmonic equation, with the help of which an explicit representation of the Green’s function of the Dirichlet problem for the polyharmonic equation in the unit ball is given for all space dimensions except for some finite set. On the basis of the obtained Green’s function, the solution of the homogeneous Dirichlet problem in the unit ball is constructed. As an example, an explicit form of the solution of the homogeneous Dirichlet problem for the inhomogeneous polyharmonic equation with the simplest polynomial right-hand side is found.

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Lyakhov, L. N., and A. V. Ryzhkov. "Solutions of theB-polyharmonic equation." Differential Equations 36, no. 10 (2000): 1507–11. http://dx.doi.org/10.1007/bf02757391.

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Xiao, Jing-En, Cheng-Yu Ku, and Chih-Yu Liu. "Solving Inverse Problems of Stationary Convection–Diffusion Equation Using the Radial Basis Function Method with Polyharmonic Polynomials." Applied Sciences 12, no. 9 (2022): 4294. http://dx.doi.org/10.3390/app12094294.

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In this article, the radial basis function method with polyharmonic polynomials for solving inverse problems of the stationary convection–diffusion equation is presented. We investigated the inverse problems in groundwater pollution problems for the multiply-connected domains containing a finite number of cavities. Using the given data on the part of the boundary with noises, we aim to recover the missing boundary observations, such as concentration on the remaining boundary or those of the cavities. Numerical solutions are approximated using polyharmonic polynomials instead of using the certa

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Karachik, Valery. "On Green’s Function of the Dirichlet Problem for the Polyharmonic Equation in the Ball." Axioms 12, no. 6 (2023): 543. http://dx.doi.org/10.3390/axioms12060543.

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The paper gives an explicit representation of the Green’s function of the Dirichlet boundary value problem for the polyharmonic equation in the unit ball. The solution of the homogeneous Dirichlet problem is found. An example of solving the homogeneous Dirichlet problem with the simplest polynomial right-hand side of the polyharmonic equation is given.

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Begehr, Heinrich, and Evgenija Gaertner. "A Dirichlet Problem for the Inhomogeneous Polyharmonic Equation in the Upper Half Plane." gmj 14, no. 1 (2007): 33–52. http://dx.doi.org/10.1515/gmj.2007.33.

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Abstract On the basis of a higher order integral representation formula related to the polyharmonic differential operator and obtained through a certain polyharmonic Green function, a Dirichlet problem is explicitly solved in the upper half plane.

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Trofymenko, Olga, and Yuliia Perevierzieva. "Mean value theorems for polyharmonic functions." Proceedings of the Institute of Applied Mathematics and Mechanics NAS of Ukraine 35 (January 28, 2022): 173–78. http://dx.doi.org/10.37069/10.37069/1683-4720-2021-35-13.

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The problem of characterization of polyharmonic functions by mean value expressions is analyzed. A sufficient condition for the biharmonic function is formulated and proved in the paper. Mean value theorems and their operators have various applications in function theory (approximation of functions, description of functional spaces) and in the qualitative theory of linear differential equations with partial derivatives (boundary properties, elimination of features, differential properties of solutions, etc.). The main properties of polyharmonic functions, in particular, properties with mean va

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Turmetov, B. Kh, and V. V. Karachik. "ON A DIRICHLET PROBLEM FOR A NONLOCAL POLYHARMONIC EQUATION." Bulletin of the South Ural State University series "Mathematics. Mechanics. Physics" 13, no. 2 (2021): 37–45. http://dx.doi.org/10.14529/mmph210206.

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The paper studies the solvability conditions for one class of boundary value problems for a nonlocal polyharmonic equation in the unit ball with Dirichlet conditions on the boundary generated by a certain orthogonal matrix. The existence and uniqueness of the solution to the posed Dirichlet problem are investigated and the Green's function is constructed. First, some auxiliary statements are established: the inversability of the Vandermonde matrix of the m-th roots of unity is investigated, then the eigenvectors and eigenvalues of the auxiliary matrix generated by the coefficients of the nonlo

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Kumar, Ajay, and Ravi Prakash. "Dirichlet problem for inhomogeneous polyharmonic equation." Complex Variables and Elliptic Equations 53, no. 7 (2008): 643–51. http://dx.doi.org/10.1080/17476930801950228.

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Dissertations / Theses on the topic "Polyharmonic equation"

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Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Thesis, Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150/document.

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Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet d

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Mtiri, Foued. "Études des solutions de quelques équations aux dérivées partielles non linéaires via l'indice de Morse." Electronic Thesis or Diss., Université de Lorraine, 2016. http://www.theses.fr/2016LORR0150.

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Cette thèse porte principalement sur l'étude des solutions de certaines équations aux dérivées partielles elliptiques via l'indice de Morse, y compris des solutions stables, i.e. quand l'indice de Morse est égal à zéro. Elle comporte deux parties indépendantes.Dans la première partie, sous des hypothèses sur-linéaires et sous-critiques sur f, on établit d'abord une estimation explicite de la norme L [infini] des solutions de -Δu = f(u) avec u = 0 sur le bord, via leurs indices de Morse. On propose une approche plus transparente et plus souple que le travail de Yang [1998], ce qui nous permet d

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Yang, Sze-Guang, and 楊世光. "Existence and Behavior for Solutions Of Polyharmonic Equations." Thesis, 2007. http://ndltd.ncl.edu.tw/handle/13142215450234081527.

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博士<br>國立中央大學<br>數學研究所<br>95<br>This dissertation is concerned with the existence and behavior for solutions of some polyharmonic equations. It is divided into two parts according to the difference of problems to which the author has devoted. The first part includes the study of a polyharmonic problem in a punctured domain. The second contains subjects about the existence of multiple solutions of some nonlinear higher order equations whose nonlinearities are assumed to be negative near the origin. In Chapter 1 we prove a divergence-type identity for positive solutions of a certain type of equa

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Books on the topic "Polyharmonic equation"

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Hans-Christoph, Grunau, and Sweers Guido, eds. Polyharmonic boundary value problems: Positivity preserving and nonlinear higher order elliptic equations in bounded domains. Springer, 2010.

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Multivariate Polysplines: Applications to Numerical and Wavelet Analysis. Academic Press, 2001.

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Kounchev, Ognyan. Multivariate Polysplines: Applications to Numerical and Wavelet Analysis. Academic Press, 2001.

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Kounchev, Ognyan. Multivariate Polysplines: Applications to Numerical and Wavelet Analysis. Elsevier Science & Technology Books, 2001.

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Book chapters on the topic "Polyharmonic equation"

1

Balk, M. B., and M. Ya Mazalov. "On Uniqueness Conditions for Entire Polyharmonic Functions." In Partial Differential and Integral Equations. Springer US, 1999. http://dx.doi.org/10.1007/978-1-4613-3276-3_16.

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Mayboroda, Svitlana, and Vladimir Maz’ya. "Pointwise Estimates for the Polyharmonic Green Function in General Domains." In Analysis, Partial Differential Equations and Applications. Birkhäuser Basel, 2009. http://dx.doi.org/10.1007/978-3-7643-9898-9_12.

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Kozlov, V., V. Maz’ya, and J. Rossmann. "The Dirichlet problem for the biharmonic and polyharmonic equations." In Mathematical Surveys and Monographs. American Mathematical Society, 2000. http://dx.doi.org/10.1090/surv/085/07.

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Kounchev, O. I. "Harmonicity Modulus and Applications to the Approximation by Polyharmonic Functions." In Approximation by Solutions of Partial Differential Equations. Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-011-2436-2_12.

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Popivanov, Petar, and Angela Slavova. "Several Properties of the Solutions of Linear and Semilinear Harmonic and Polyharmonic Equations." In Springer Proceedings in Mathematics & Statistics. Springer International Publishing, 2023. http://dx.doi.org/10.1007/978-3-031-21484-4_14.

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Grunau, Hans-Christoph, and Guido Sweers. "The Maximum Principle and Positive Principal Eigenfunctions for Polyharmonic Equations." In Reaction Diffusion Systems. CRC Press, 2020. http://dx.doi.org/10.1201/9781003072195-15.

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Conference papers on the topic "Polyharmonic equation"

1

Karachik, V. V., and B. Kh Turmetov. "On a class of Neumann type problems for polyharmonic equation." In PROCEEDINGS OF THE 45TH INTERNATIONAL CONFERENCE ON APPLICATION OF MATHEMATICS IN ENGINEERING AND ECONOMICS (AMEE’19). AIP Publishing, 2019. http://dx.doi.org/10.1063/1.5133491.

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Turmetov, Batirkhan, and Valery Karachik. "On sufficient solvability conditions for Neumann type problems for polyharmonic equation in a ball." In INTERNATIONAL UZBEKISTAN-MALAYSIA CONFERENCE ON “COMPUTATIONAL MODELS AND TECHNOLOGIES (CMT2020)”: CMT2020. AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0057206.

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Koshanov, Bakytbek Danebekovich. "On the solvability of boundary value problems for the nonhomogeneous polyharmonic equation in a ball." In INTERNATIONAL CONFERENCE ON ANALYSIS AND APPLIED MATHEMATICS (ICAAM 2014). AIP Publishing LLC, 2014. http://dx.doi.org/10.1063/1.4893815.

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Kanguzhin, Baltabek, Niyaz Tokmagambetov, and Nurken Bekbayev. "The Green function and correctly solvable non–local boundary value problems for the polyharmonic equation in a punctured domain." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930527.

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Bartsch, Thomas. "Critical equations for the polyharmonic operator." In Proceedings of the ICM 2002 Satellite Conference on Nonlinear Functional Analysis. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812704283_0004.

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KARAKILIÇ, Sedef, and Setenay AKDUMAN. "On the eigenvalues of a polyharmonic matrix operator near diffraction planes." In SEVENTH INTERNATIONAL CONFERENCE ON NEW TRENDS IN THE APPLICATIONS OF DIFFERENTIAL EQUATIONS IN SCIENCES (NTADES 2020). AIP Publishing, 2021. http://dx.doi.org/10.1063/5.0040407.

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Koshanov, Bakytbek D., and Maira D. Koshanova. "On the representation of the Green function of the Dirichlet problem and their properties for the polyharmonic equations." In ADVANCEMENTS IN MATHEMATICAL SCIENCES: Proceedings of the International Conference on Advancements in Mathematical Sciences. AIP Publishing LLC, 2015. http://dx.doi.org/10.1063/1.4930446.

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