Renormalized solutions for a class of nonlinear parabolic equations without sign condition involving nonstandard growth

Abstract

An existence result of a renormalized solution for a class of doubly nonlinear parabolic equations with variable exponents is established. The main contribution of our work is to prove the existence of a renormalized solution without the sign condition and the coercivity condition on the nonlinearity H. The second term $f$ belongs to $L^1(Q)$ and $b(u_0)\in L^1(\Omega)$.