On anisotropic parabolic equations with a nonlinear convection term depending on the spatial variable

Abstract

Abstract Consider an anisotropic parabolic equation with a nonlinear convection term depending on the spatial variable. If the diffusion coefficients are degenerate, in general, the boundary trace cannot be defined for the weak solution. The existence and the uniqueness of weak solution are researched without the boundary value condition. Moreover, a general method to prove stability of weak solutions independent of the boundary value condition is introduced for the first time.

Keywords

• Anisotropic parabolic equation
• Nonlinear convection term
• Boundary value condition