Partial differential inclusions with spatially variable exponents and large diffusion

Abstract

In this work we prove continuity of the flows and upper semicontinuity of global attractors for large diffusion when the variable exponent go to a constant $p>2$ for inclusions of the form $$\displaystyle\frac{\partial u}{\partial t} - div(D|\nabla u|^{p(x)-2}\nabla u) + |u|^{p(x)-2}u\in F(u).$$