SOLVABILITY OF DEGENERATED p(x)-PARABOLIC EQUATIONS WITH THREE UNBOUNDED NONLINEARITIES.
Vol. 4(1) Jan. 2016, No. 5, pp. 42-62
Y. AKDIM , C. ALLALOU, N. EL GORCH
In this paper, we study the existence of renormalized solutions for the nonlinear p(x)-parabolic problem with f ∈ L1(Q) and b(x, u0) ∈ L1(Ω). The main contribution of our work is to prove the existence of renormalized solutions of the weighted variable exponent Sobolev spaces and we suppose that H(x, t, u, ∇u) is the nonlinear term satisfying some growth condition but no sign condition or the coercivity condition.