An optimal Liouville-type theorem of the quasilinear parabolic equation with a p-Laplace operator

作者：Zhang Zhengce^*; Li Zhenjie

来源：Nonlinear Analysis-Theory Methods & Applications, 2011, 74(16): 5735-5744.

DOI：10.1016/j.na.2011.05.063

• Liouville-type theorem
• Parabolic equation
• p-Laplace

In this paper, we consider nonnegative solutions of the quasilinear parabolic equation with p-Laplace operator u(t) = div(vertical bar del u vertical bar(p-2)del u) + vertical bar u vertical bar(q-1)u, where p > 2 and q > p - 1. Our main result is that there is no nontrivial positive bounded radial entire solution. The proof is based on intersection comparison arguments, which can be viewed as a sophisticated form of the maximum principle and has been used to deal with the semilinear heat equation by Polacik and Quittner [Peter Polacik, Pavol Quittner, A Liouville-type theorem and the decay of radial solutions of a semilinear heat equation, Nonlinear Analysis TMA 64 (2006) 1679-1689] and the porous medium equation by Souplet [Ph. Souplet, An optimal Liouville-type theorem for radial entire solutions of the porous medium equation with source, J. Differential Equations 246 (2009) 3980-4005].

• 出版日期2011-11
• 单位西安交通大学