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Pré-Publication, Document De Travail Année : 2015

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

Résumé

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 $q>1$. 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 $a,b>0$, $11$.
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Dates et versions

hal-01006258 , version 1 (14-06-2014)
hal-01006258 , version 2 (29-06-2014)
hal-01006258 , version 3 (26-11-2015)

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Quoc-Hung Nguyen, Laurent Veron. Wiener criteria for existence of large solutions of nonlinear parabolic equations with absorption in a non-cylindrical domain. 2015. ⟨hal-01006258v3⟩
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