Well-posed solvability of the Cauchy problem for difference equations of parabolic type

DOI10.1016/0362-546X(94)E0004-ZzbMath0818.65047MaRDI QIDQ4328323

Allaberen Ashyralyev, Pavel E. Sobolevskii

Publication date: 15 August 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

zbMATH Keywords

abstract Cauchy problemdifference schemeBanach spacewell-posed solvabilitycoercive inequalitiesevolutionary partial differential equationsunbounded strongly positive operator

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Numerical solutions to equations with linear operators (65J10) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Linear differential equations in abstract spaces (34G10) Initial value problems for linear higher-order PDEs (35G10) Finite difference and finite volume methods for ordinary differential equations (65L12) Higher-order parabolic equations (35K25)

Related Items

ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS INL^P([0,T;E) SPACES], Error estimates for projection-difference methods for differential equations with differentiable operators, A note on the stability of the integral-differential equation of the parabolic type in a Banach space, Well-posedness of the boundary value problem for parabolic equations in difference analogues of spaces of smooth functions, A note on the parabolic differential and difference equations, A note on the second order of accuracy difference schemes for hyperbolic--parabolic equations, Stability of difference schemes for hyperbolic-parabolic equations

Cites Work

• Difference schemes of optimal type for the approximate solution of parabolic equations
• A note on the difference schemes for hyperbolic equations
• High-Accuracy Stable Difference Schemes for Well-Posed Initial-Value Problems
• Single step methods for inhomogeneous linear differential equations in Banach space
• On Rational Approximations of Semigroups
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