Regularity and uniqueness results in grand Sobolev spaces for parabolic equations with measure data

In this paper we prove some regularity and uniqueness results for a class of nonlinear parabolic problems whose prototype is [GRAPHICS] where Q is the cylinder Q = (0, T) x Omega, T > 0, Omega subset of R-N, N greater than or equal to 2, is an open bounded set having C-2 boundary, mu is an element of L-1(0, T; M(Omega)) and u(0) belongs to M(Omega), the space of the Radon measures in Omega, or to L-1(Omega). The results are obtained in the framework of the so-called grand Sobolev spaces, and represent an extension of earlier results on standard Sobolev spaces