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Finite superelements method for biharmonic equation
Mathematical Modelling and Analysis, 2007 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
Mikhail Galanin +2 more
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On the Schrodinger equations with isotropic and anisotropic fourth-order dispersion
Electronic Journal of Differential Equations, 2016 This article concerns the Cauchy problem associated with the nonlinear fourth-order Schrodinger equation with isotropic and anisotropic mixed dispersion.
Elder J. Villamizar-Roa, Carlos Banquet
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An inverse problem for biharmonic equation [PDF]
International Journal of Mathematics and Mathematical Sciences, 1988 An inhomogeneity immersed in a medium is found from the measurements of the elastic field on the surface of the medium.
A. G. Ramm
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Ground state solutions for p-biharmonic equations
Electronic Journal of Differential Equations, 2017 In this article we study the p-biharmonic equation $$ \Delta_p^2u+V(x)|u|^{p-2}u=f(x,u),\quad x\in\mathbb{R}^N, $$ where $\Delta_p^2u=\Delta(|\Delta u|^{p-2}\Delta u)$ is the p-biharmonic operator.
Xiaonan Liu +2 more
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On a Boundary Value Problem for the Biharmonic Equation with Multiple Involutions
Mathematics, 2021 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 ...
Batirkhan Turmetov +2 more
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Linear barycentric rational collocation method for solving biharmonic equation
Demonstratio Mathematica, 2022 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.
Li Jin
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Blow-up phenomena for a p(x)-biharmonic heat equation with variable exponent [PDF]
Mathematica Moravica, 2023 In this paper, we deal with a p(x)-biharmonic heat equation with variable exponent under Dirichlet boundary and initial condition. We prove the blow up of solutions under suitable conditions.
Pişkin Erhan, Butakin Gülistan
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Biharmonic Nonlinear Scalar Field Equations
International Mathematics Research Notices, 2022 Abstract We prove a Brezis–Kato-type regularity result for weak solutions to the biharmonic nonlinear equation $$ \begin{align*} & \Delta^2 u = g(x,u)\qquad\text{in }\mathbb{R}^N\end{align*}$$with a Carathéodory function $g:\mathbb {R}^N\times \mathbb {R}\to \mathbb {R}$, $N\geq 5$.
Mederski, Jarosław, Siemianowski, Jakub
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σ-monogenic functions in commutative algebras
Pracì Mìžnarodnogo Geometričnogo Centru, 2023 In finite-dimensional commutative associative algebra, the concept of σ-monogenic function is introduced. Necessary and sufficient conditions for σ-monogeneity have been established.
Vitalii Shpakivskyi
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A generalized nonlinear Picone identity for the p-biharmonic operator and its applications
Journal of Inequalities and Applications, 2019 A generalized nonlinear Picone identity for the p-biharmonic operator is established in this paper. As applications, a Sturmian comparison principle to the p-biharmonic equation with singular term, a Liouville’s theorem to the p-biharmonic system, and a ...
Tingfu Feng
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