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

[摘要] We consider the following nonlinear parabolic equation , whereand the exponent of nonlinearityare 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.

[学科分类] 几何与拓扑