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

We obtain a necessary condition and a sufficient condition, both expressed in terms of Wiener type tests involving the parabolic Wq′2,1-capacity, where q′=qq−1 and q>1q>1, for the existence of large solutions to equation ∂tu−Δu+uq=0∂tu−Δu+uq=0 in a non-cylindrical domain. We provide also a sufficient condition for the existence of such solutions to equation ∂tu−Δu+eu−1=0∂tu−Δu+eu−1=0. Besides, we apply our results to equation: ∂tu−Δu+a|∇u|p+buq=0∂tu−Δu+a|∇u|p+buq=0 for a,b>0a,b>0, 11q>1.