Existence Results for A Nonlinear  Degenerate Parabolic Equation involving  -Laplacian Type Diffusion Process

In this study, a nonlinear degenerate parabolic equation is used to describe a nonlinear -Laplacian equation process that arises in many areas of science and engineering in mechanics, quantum physics, and chemical design. This work has the objective of proving the existence of the local weak solution of a nonlinear p(x)-Laplacian equation by the compactness theorem. The uniformly local characteristics of the solutions for the gradients by estimating the regularization problem and using the Moser iterative techniques. Moreover, some properties of the local solutions depend on uniformly bounded situations and the -norm to the gradient is considered.