Nonlinear degenerate diffusion problems with a singularity

Nonlinear Degenerate Diffusion Problems

Self similar solutions u(x,t) = f(x//t) of the one-dimensional porousmedium equation are studied in this paper. These solutions emerge frominitial values that consist of two constant states: one non-positive forx < 0 and one non-negative for x > 0. With a diffusivity of the form|u| , we consider for m > 0 sign change solutions and for m e (-1,0]non-negative solutions. Th...

Numerical Methods for Fourth Order Nonlinear Degenerate Diffusion Problems

Numerical schemes are presented for a class of fourth order diffusion problems. These problems arise in lubrication theory for thin films of viscous fluids on surfaces. The equations being in general fourth order degenerate parabolic, additional singular terms of second order may occur to model effects of gravity, molecular interactions or thermocapillarity. Furthermore, we incorporate nonlinea...

High-Order Relaxation Schemes for Nonlinear Degenerate Diffusion Problems

Several relaxation approximations to partial differential equations have been recently proposed. Examples include conservation laws, HamiltonJacobi equations, convection-diffusion problems, gas dynamics problems. The present paper focuses onto diffusive relaxation schemes for the numerical approximation of nonlinear parabolic equations. These schemes are based on a suitable semilinear hyperboli...

Viscosity Solutions to Degenerate Diffusion Problems

This paper concerns the weak solutions to a Cauchy problem in RN for a degenerate nonlinear parabolic equation. We obtain the Hölder regularity of the weak solutions to this problem.

Moving Boundary Problems with Nonlinear Diffusion