Quenching for Porous Medium Equations

Hamilton’s gradient estimates and Liouville theorems for porous medium equations

Continuity estimates for porous medium type equations with measure data

We consider parabolic equations of porous medium type of the form ut − divA(x, t, u,Du) = μ in ET , in some space time cylinderET . The most prominent example covered by our assumptions is the classical porous medium equation ut −∆u = μ in ET . We establish a sufficient condition for the continuity of u in terms of a natural Riesz potential of the right-hand side measure μ. As an application we...

Globally Convergent Multigrid Methods for Porous Medium Type Equations

On Dual-Finite Volume Methods for Extended Porous Medium Equations

This article shows that the unconditional stability of the Dual-Finite Volume Method, which is at least valid for linear problems, is not true for generic nonlinear differential equations including the PMEs unless the coefficient appearing in the numerical fluxes are appropriately evaluated. This article provides a theoretically truly isotone numerical fluxes specialized for solving the PMEs pr...

Quenching Rate for the Porous Medium Equation with a Singular Boundary Condition

We study the porous medium equation   = , 0 < < , > m t x t  0 t xx . We prove finite time quenching for the solution at the boundary . We also estabu u with a singular boundary condition       0, = 0, m x u t u   = 0 x lish the quenching rate and asymptotic behavior on the quenching point.