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arXiv · 1406.3850

Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain

Quoc-Hung Nguyen·Laurent Veron
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Abstract

We obtain a necessary and a sufficient condition expressed in terms of Wiener type tests involving the parabolic $W\_{q'}^{2,1}$- capacity, where $q'=\frac{q}{q-1}$, for the existence of large solutions to equation $\prt\_tu-\Delta u+u^q=0$ in non-cylindrical domain, where $q\textgreater{}1$. Also, we provide a sufficient condition associated with equation $\prt\_tu-\Delta u+e^u-1=0$ . Besides, we apply our results to equation: $\prt\_tu-\Delta u+a|\nabla u|^p+bu^{q}=0$ for $a,b\textgreater{}0$, $11$.

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Quoc-Hung Nguyen, Laurent Veron. 2014-06-15. Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain. https://arxiv.org/abs/1406.3850

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