Uniqueness of a very singular solution to nonlinear degenerate parabolic equations with absorption for Dirichlet boundary condition

Abstract

We prove the existence and uniqueness of singular solutions (fundamental solution, very singular solution, and large solution) of quasilinear parabolic equations with absorption for Dirichlet boundary condition. We also show the short time behavior of singular solutions as t tends to 0.

Keywords

• Degenerate parabolic equations
• large solution
• very singular solution
• Dirac measure