The porous medium equation with variable exponent revisited

Abstract

The author presents a simplified proof for the local continuity of the weak solutions to the porous medium equation with variable positive bounded exponent $\gamma (x,t)$

$$\begin{aligned} u_t-\nabla \cdot \left( |u|^{\gamma (x,t)} \, \nabla u\right) =0 , \quad \mathrm {in} \quad \Omega _T =\Omega \times (0,T] , 0<T<\infty . \end{aligned}$$

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