A nonlinear parabolic equation with a nonlocal boundary term

DOI10.1016/j.cam.2009.07.059zbMath1189.65212OpenAlexW2149371632MaRDI QIDQ961537

Marián Slodička, Sofiane Dehilis

Publication date: 31 March 2010

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2009.07.059

zbMATH Keywords

stabilityconvergencenumerical examplenonlinear parabolic equationsolvabilitythermoelasticitymethod of linesnonlocal boundary conditionRothe' s method

Mathematics Subject Classification ID

Nonlinear parabolic equations (35K55) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)

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Cites Work

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• Finite difference methods for a nonlocal boundary value problem for the heat equation
• Finite difference approximations for a class of nonlocal parabolic equations
• Stability in the numerical solution of the heat equation with nonlocal boundary conditions
• Numerical solution of the heat equation with nonlocal boundary conditions
• Generalized quasilinearization method for reaction-diffusion equations under nonlinear and nonlocal flux conditions
• A numerical approach for a semilinear parabolic equation with a nonlocal boundary condition
• Global solvability of a nonlinear nonstationary problem with a nonlocal boundary condition of radiative heat transfer type
• A High-Order Difference Scheme for a Nonlocal Boundary-Value Problem for the Heat Equation
• A decreasing property of solutions of parabolic equations with applications to thermoelasticity
• Monotonic decay of solutions of parabolic equations with nonlocal boundary conditions
• Extensions of a property of the heat equation to linear thermoelasticity and other theories
• Remarks on a paper by W. A. Day on a maximum principle under nonlocal boundary conditions
• Numerical solutions of reaction-diffusion equations with nonlocal boundary conditions

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