*Published Paper*

**Inserted:** 22 jul 2018

**Last Updated:** 22 jul 2018

**Journal:** J. Differential Equations

**Pages:** 40

**Year:** 2016

**Doi:** https://www.sciencedirect.com/science/article/pii/S002203961500649X

**Abstract:**

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 $q>1$.

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