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In this note we consider a parabolic evolution equation in a polygonal space-time cylinder. We show, that the elliptic part is given by a  m -accretive mapping from  L q  ( Ω ) →  L q  ( Ω ). Therefore we can apply the theory of nonlinear semigroups in Banach spaces in order to get regularity results in time and space.

journal of numerical mathematics

Regularity results and numerical solution by the discontinuous Galerkin method to semilinear parabolic initial boundary value problems with nonlinear Newton boundary conditions in a polygonal space-time cylinder