Geodesic
Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data
Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 703-713.

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The purpose of this paper is to derive the error estimates for discretization in time of a semilinear parabolic equation in a Banach space. The estimates are given in the norm of the space $\Bbb X_{\alpha }$ for $0\alpha 1$ when the initial condition is not regular.
Classification : 34G20, 35G10, 35K22, 35K25, 35R20, 65J15, 65M15, 65M20
Keywords: error estimates; parabolic equation; backward Euler method; nonsmooth initial data 
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     title = {Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data},
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Slodička, Marian. Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) no. 4, pp. 703-713. http://geodesic.mathdoc.fr/item/CMUC_1991__32_4_a12/