Stability and existence results for a class of nonlinear parabolic equations with three lower order terms and measure data using Lorentz spaces

We study both existence and stability of renormalized solutions for nonlinear parabolic problems with three lower order terms that have, respectively, growth with respect to u and to the gradient, whose model (P) {u(t) - Delta(p)u - div[c(t, x)vertical bar u vertical bar(gamma-1)u] + b(t, x)vertical bar del u vertical bar(lambda) + d(t, x)vertical bar u vertical bar(iota) = mu - div(E) in Q, u(0, x) = u(0)(x) in Omega, u(t, x) = 0 on (0, T) x partial derivative Omega where Q := (0, T)x Omega (with Omega is an open bounded subset of R-N (N >= 2) and T > 0), 1 < p < N, Delta(p) is the usual p-Laplace operator, and mu is an element of M(Q) is a (general) measure with bounded total variation on Q. As a consequence of our main results, we prove that the conditions gamma = (N+2)(p-1)/N+p, lambda = N(p-1)+p/N+2, 0 <= iota <= p - N-p/N, c is an element of L tau=N+p/p-1 (Q)(N), b is an element of L-N+2,L-1(Q) and d is an element of L-z'(,1)(Q) (with z = pN-N-p/iota N) are necessary and sufficient for the existence and the stability of solutions for every sufficiently regular u(0) is an element of L-2(Omega), E is an element of L-p' (Q)(N) and irregular mu is an element of M(Q).