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Ashyralyev, Allaberen; Piskarev, Serguei; Weis, Lutz

On well-posedness of difference schemes for abstract parabolic equations in \(L^p([0,T];E)\) spaces. (English) Zbl 1022.65095

Numer. Funct. Anal. Optimization 23, No. 7-8, 669-693 (2002).
The paper deals with establishing of a coercive inequality in the discrete space \(L_{\tau_n}^p ([0,T];E_n)\). To this end the authors consider a general approximation scheme based on semigroup theory and functional analysis tools.
Reviewer: Emil Minchev (Chiba)

Cited in 34 Documents

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
35K90 Abstract parabolic equations

Keywords:

difference scheme; abstract parabolic equations; coercive inequality; semigroup theory
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\textit{A. Ashyralyev} et al., Numer. Funct. Anal. Optim. 23, No. 7--8, 669--693 (2002; Zbl 1022.65095)
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