2017
Том 69
№ 6

All Issues

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

Boldovskaya O. M.

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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.

English version (Springer): Ukrainian Mathematical Journal 62 (2010), no. 7, pp 1040-1060.

Citation Example: Boldovskaya O. M. Removability of an isolated singularity of solutions of the Neumann problem for quasilinear parabolic equations with absorption that admit double degeneration // Ukr. Mat. Zh. - 2010. - 62, № 7. - pp. 894–912.

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