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

作者：Quoc Hung Nguyen; Veron Laurent

来源：Journal of Differential Equations, 2016, 260(5): 4805-4844.

DOI：10.1016/j.jde.2015.11.032

• Bessel capacities
• Hausdorff capacities
• Parabolic boundary
• Riesz potential
• Maximal solutions

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' = q/q-1 and q > 1, for the existence of large solutions to equation partial derivative(t)u - Delta u + u(q) = 0 in a non-cylindrical domain. We provide also a sufficient condition for the existence of such solutions to equation partial derivative(t)u - Delta u + e(u) - 1 = 0. Besides, we apply our results to equation: atu -Delta u + a vertical bar del u vertical bar(p) + bu(q) = 0 for a,b > 0, 1 < p < 2 and q >1.

• 出版日期2016-3-5