Global solvability for semilinear anisotropic evolution partial differential equations

In this paper we consider the Cauchy problem for a class of semilinear anis otropic evolution equations with parabolic linear part. Using standard tech niques we reduce our problem in an integral form. Thus a local L-2 solution is given as fixed point of the correspondent integral operator, defined fo r t is an element of (0, T-1]. Taking as initial datum the solution evalued in T-1, we find a local L-2 solution, defined for t is an element of [T-1, 2T(1)]. Iterating this process and patching together all the local solutio ns defined on intervals of type [nT(1), (n + 1)T-1], with n is an element o f N, we obtain a global solution defined for every t greater than or equal to 0. We point out that our paper recaptures the results in Tadmor [8] as a particular case.