Well-posedness of parabolic differential and difference equations. (English) Zbl 1201.35064
Summary: We consider the abstract parabolic differential equation , in a Banach space with - the infinitesimal generator of an analytic, exponentially decreasing semigroup . The main purpose of this paper is to establish the well-posedness of this equation in , , and the well-posedness of the corresponding Rothe difference scheme in , . Moreover, we apply our theoretical results to obtain new coercivity inequalities for the solution of parabolic difference equations.
|35B65||Smoothness and regularity of solutions of PDE|
|65M06||Finite difference methods (IVP of PDE)|