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Zbl 1022.65095
Ashyralyev, Allaberen; Piskarev, Serguei; Weis, Lutz
On well-posedness of difference schemes for abstract parabolic equations in $L^p([0,T];E)$ spaces.
(English)
[J] Numer. Funct. Anal. Optimization 23, No.7-8, 669-693 (2002). ISSN 0163-0563; ISSN 1532-2467/e

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.
[Emil Minchev (Chiba)]
MSC 2000:
*65M06 Finite difference methods (IVP of PDE)
35K90 Abstract parabolic evolution equations

Keywords: difference scheme; abstract parabolic equations; coercive inequality; semigroup theory

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