Existence of Solutions for the Evolution p(x)‎-Laplacian Equation Not in Divergence Form

الملخص EN

The existence of weak solutions is studied to the initial Dirichlet problemof 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.