Abstract: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.
Keywords: error estimates, parabolic equation, backward Euler method, nonsmooth initial data
AMS Subject Classification: 65M15, 35K22, 65M20