Existence of a solution for a class of parabolic equations with three unbounded nonlinearities, natural growth terms and \(L^1\) data (Q465024)

The authors give a proof of the existence of a renormalized solution for a class of nonlinear parabolic equations with \(p\)-growth in the gradient, without any growth assumption on \(u\) and with data in \(L^1\). The concept of renormalized solution was introduced by Lions and Di Perna. The elliptic version was intensively studied by Boccardo, Murat and their schools. The result of this paper extends, to a more general case, theorems that were proved in several other papers.