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

Abstract

We consider the following nonlinear parabolic equation:, where : Ω × (0, ) → R and the exponent of nonlinearity (⋅) 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.

On the well-posedness of generalized Darcy–Forchheimer equation

“…The applications of nonlinear differential equations are seen in many fields (see [1][2][3][4]). In the field of fluid dynamics, the nonlinear correction to Darcy's law has been an active area of research for many years.…”