Well-posedness of difference schemes for semilinear parabolic equations with weak solutions

DOI10.1134/S0965542510120079zbMath1224.35214MaRDI QIDQ3012271

Piotr P. Matus

Publication date: 5 July 2011

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

initial-boundary value problemweak solutionsdifference schemesparabolic equationsChaplygin comparison theoremBihari-type inequalities

Mathematics Subject Classification ID

Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Semilinear parabolic equations (35K58)

Related Items (6)

Unnamed Item ⋮ Consistent convergence rate estimates in the grid \(W_{2,0}^2(\omega)\) norm for difference schemes approximating nonlinear elliptic equations with mixed derivatives and solutions from \(W_{2,0}^m(\Omega)\), \(3 < m \leq 4\) ⋮ Stability with respect to the input data and monotonicity of an implicit finite-difference scheme for a quasilinear parabolic equation ⋮ On the role of conservation laws in the problem on the occurrence of unstable solutions for quasilinear parabolic equations and their approximations ⋮ Approximations to problems of optimal control of leading coefficients of elliptic equations in nondivergence form with an unbounded nonlinearity in the coefficients ⋮ Criterion for the stability of difference schemes for nonlinear differential equations

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