Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities

Abstract EN

We consider the following nonlinear parabolic equation: ut-div(|∇u|p(x)-2∇u)=f(x,t), where f:Ω×(0,T)→R and the exponent of nonlinearity p(·) are given functions.

By using a nonlinear operator theory, we prove the existence and uniqueness of weak solutions under suitable assumptions.

We also give a two-dimensional numerical example to illustrate the decay of solutions.