Existence solutions for a class of nonlinear parabolic equations with variable exponents and L^1 data

Abstract

In this article, we study the problem

(∂ b(x,u) ∕ ∂ t) - div a(x, t, u, ∇ u) + div φ(u) = f, in Ω × ]0, T],

u = 0 on ∂ Ω × ]0,T[

b(x,u)(t=0) = b(x,u₀). in Ω,

in the framework of generalized Sobolev spaces, with b(x,u) unbounded function on u. The main contribution of our work is to prove the existence of renormalized solutions when the second term f belongs to L¹(Q_T).