Renormalized Solutions of Nonlinear Degenerated Parabolic Equations Without Sign Condition and L1 Data
Authors: Youssef Akdim, Jaouad Bennouna and Mounir Mekkour
Abstract: In this paper, we study the problem:
∂u/∂t - div (a(x, t, u,Du))+ H(x, t, u,Du) = f in ΩX]0,T[, u(x,0) = u0 in Ω u = 0 in ∂ΩX]0,T[
in the framework of weighted Sobolev space. The main contribution of our work is to prove the existence of a renormalized solution without the sign condition and the coercivity condition on H(x, t, u, Du), the critical growth condition on H is with respect to Du and no growth with respect to u. The second term f belongs to L1(Q) and u0 ε L1(Ω).