Removability of an isolated singularity of solutions of the Neumann problem for quasilinear parabolic equations with absorption that admit double degeneration

Abstract

We consider the Neumann initial boundary-value problem for the equation $$u_t=\text{div}(u^{m−1}|Du|^{λ−1}Du)−u^p$$ in domains with noncompact boundary and with initial Dirac delta function. In the case of slow diffusion $(m + λ − 2 > 0)$ and critical absorption exponent $(p = m + λ − 1 +\frac{λ + 1}{N})$, we prove that the singularity at the point $(0, 0)$ is removable.