Existence of Solutions for the Evolution p(x)‐Laplacian Equation Not in Divergence Form
Changchun Liu, Junchao Gao, Songzhe Lian · Journal of Applied Mathematics · 2012
The existence of weak solutions is studied to the initial Dirichlet problem of the equation ut = udiv(|∇u|p(x)−2∇u), with inf p(x) > 2. We adopt the method of parabolic regularization. After establishing some necessary uniform estimates on the approximate solutions, we prove the existence of weak solutions.