REGULARITY OF WEAK SOLUTIONS OF SEMILINEAR PARABOLIC-SYSTEMS OF ARBITRARY ORDER

Let u be a weak solution of the initial boundary value problem for the semilinear parabolic system of order 2m : u'(t) + Au(t) + f (t, ., u, ..., del(m)u) = 0. Let f satisfy controllable growth conditions. Then u is smooth. This result is proved by a kind of continuity method, where the time t is the parameter of continuity.