Calculus of Variations and Geometric Measure Theory

Q. H. Nguyen - L. VĂ©ron

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

created by nguyen on 22 Jul 2018


Published Paper

Inserted: 22 jul 2018
Last Updated: 22 jul 2018

Journal: J. Differential Equations
Pages: 40
Year: 2016


We obtain a necessary condition and a sufficient condition, both 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 $\partial_tu-\Delta u+u^q=0$ in non-cylindrical domain, where $q>1$. Also, we provide a sufficient condition associated with equation $\partial_t u-\Delta u+e^u-1=0$. Besides, we apply our results to equation: $\partial_tu-\Delta u+a
\nabla u
^p+bu^{q}=0$ for $a,b>0$, $1<p<2$ and $q>1$.