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.
@article{118450, author = {Mari\'an Slodi\v cka}, title = {Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data}, journal = {Commentationes Mathematicae Universitatis Carolinae}, volume = {32}, year = {1991}, pages = {703-713}, zbl = {0755.65095}, mrnumber = {1159817}, language = {en}, url = {http://dml.mathdoc.fr/item/118450} }
Slodička, Marián. Smoothing effect and discretization in time to semilinear parabolic equations with nonsmooth data. Commentationes Mathematicae Universitatis Carolinae, Tome 32 (1991) pp. 703-713. http://gdmltest.u-ga.fr/item/118450/
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