In this paper, we are concerned with a doubly nonlinear anisotropic parabolic equation, in which the diffusion coefficient and the variable exponent depend on the time variable t. Under certain conditions, the existence of weak solution is proved by applying the parabolically regularized method. Based on a partial boundary value condition, the stability of weak solution is also investigated.
Zhan H, Feng Z. Existence and stability of the doubly nonlinear anisotropic parabolic equation. J Math Anal Appl. 2021;497(1):124850. doi:10.1016/j.jmaa.2020.124850
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Journal of Mathematical Analysis and Applications