On a nonlinear singular diffusion problem:existence and uniqueness

Abstract

The singular diffusion equation u_t=(u⁻¹u_x)_x:arises in many areas of application, e.g. in the central limit approximation to Carleman's model of Boltzman equation, or, in the expansion of a thermalized electron cloud in plasma physics. This paper concerns the existence and uniqueness of solution of a mixed boundary value problem of equation u_t=(u^m=1u_x)_x for −1 < m ≤0.

Keywords:

• Singular diffusion
• existence
• uniqueness
• approximation

AMS:

• 35K15
• 35K55
• 35B40

^∗Department of Mathematical Sciences,Ball State University, Municie, IN 47306

^∗Department of Mathematical Sciences,Ball State University, Municie, IN 47306

Notes

^∗Department of Mathematical Sciences,Ball State University, Municie, IN 47306

Additional information

Notes on contributors

Hongfei Zhang

∗