The Evolutionary p(x)‎-Laplacian Equation with a Partial Boundary Value Condition

الملخص EN

Consider a diffusion convection equation coming from the electrorheological fluids.

If the diffusion coefficient of the equation is degenerate on the boundary, generally, we can only impose a partial boundary value condition to ensure the well-posedness of the solutions.

Since the equation is nonlinear, the partial boundary value condition cannot be depicted by Fichera function.

In this paper, when α

The stability of the solutions, dependent on this partial boundary value condition, is obtained.

While α>p+-1, the stability of the solutions is obtained without the boundary value condition.

At the same time, only if α>0 and p->1 can the uniqueness of the solutions be proved without any boundary value condition.