Removability of an isolated singularity of solutions of the Neumann problem for quasilinear parabolic equations with absorption that admit double degeneration
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 +\fr...
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| Datum: | 2010 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Russisch Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2010
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2923 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
| Завантажити файл: |  |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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