Existence of solutions for some doubly degenerate parabolic equations with natural growth terms

This paper deals with a class of doubly degenerate parabolic equations of the type ∂b(u)∂t−div(a(x,t,u,∇u))+F(x,t,u,∇u)=f, where bb is a strictly increasing C1C1-function. Under some suitable hypothesis, we prove that there exists at least a bounded solution to this problem in standard weak sense.