Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization

Abstract

We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: [Formula: see text] which involves a quasilinear elliptic operator of Leray–Lions type with variable exponents. Next, we discuss the global behavior of solutions and in particular the convergence to a stationary solution as [Formula: see text].