ON WELL-POSEDNESS OF DIFFERENCE SCHEMES FOR ABSTRACT PARABOLIC EQUATIONS IN L P ([0,T]; E) SPACES

ABSTRACT This paper is devoted to the numerical analysis of abstract parabolic differential equations in -spaces. The presentation uses general approximation scheme and is based on semigroup theory and a functional analysis approach. For the solutions of the first and second order of accuracy difference schemes, the almost coercive inequality in spaces with the factor are obtained. In the case of UMD space E n we establish a coercive inequality in under the condition of R-boundedness.

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