Quasilinear parabolic problem with variable exponent: Qualitative analysis and stabilization
Résumé
We discuss the existence and uniqueness of the weak solution of the following nonlinear parabolic problem: (PT) ut -∇·a(x,∇u) = f(x,u)in QT =def(0,T) × ω,u = 0 on =T =def(0,T) × ∂ω,u(0,x) = u0(x) in ω, 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 t →∞. © 2018 World Scientific Publishing Company.