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

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 $a,b\textgreater{}0$, $11$.