We consider the following nonlinear parabolic equation: , where 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.
"Well-Posedness and Numerical Study for Solutions of a Parabolic Equation with Variable-Exponent Nonlinearities." Int. J. Differ. Equ. 2018 (SI2) 1 - 9, 2018. https://doi.org/10.1155/2018/9754567