Entropy solutions for parabolic problems in Musielak framework without using the sign condition of the nonlinearities

Abstract

We prove in this paper the existence of solutions of nonlinear parabolic problems in inhomogeneous Musielak Orlicz Sobolev spaces, we assume neither a ${\Delta }_2$ nor ${\nabla }_2$ on the Musielak function $\phi$. The main contribution of our work is to prove the existence of entropy solutions without the sign condition on the nonlinearity. The second term $f$ belongs to $L^1(Q)$.

not correct

References in corpus (1)

• Existence of renormalized solutions to elliptic equation in Musielak-Orlicz space