Preprint A673/2010
Homogenization of Degenerate Porous Medium Type Equations in Ergodic Algebras
Jean Carlos Silva | Frid, Hermano
Keywords: two-scale Young Measures | homogenization | algebra with mean value | Porous medium equation
We consider the homogenization problem for general porous medium type equations of the form $u_t=\D f(x,\dfrac{x}{\ve}, u)$, where $f(x,y,\cdot)$ is increasing but may degenerate in the sense that $f_u(x,y,\cdot)$ may vanish on a set with empty interior. We address both, the Cauchy problem and the initial-boundary value problem, with null boundary condition. The homogenization is carried out in the general context of ergodic algebras.