Liouville-type theorems for nonlinear degenerate parabolic equation

被引：0
|
作者：
Quoc Hung Phan [1 ]
机构：
[1] Duy Tan Univ, Inst Res & Dev, Da Nang, Vietnam
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2016年 / 16卷 / 03期
关键词：
Degenerate parabolic equation; Nonexistence; Liouville-type theorem; p-Laplacian; LINEAR ELLIPTIC-EQUATIONS; POROUS-MEDIUM EQUATION; P-LAPLACIAN EQUATIONS; SUPERLINEAR PROBLEMS; RADIAL SOLUTIONS; CAUCHY-PROBLEM; BLOW-UP; SINGULARITY; SYSTEMS; DECAY;
D O I：
10.1007/s00028-015-0311-5
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study Liouville-type theorems for degenerate parabolic equation of the form where and . We prove the optimal Liouville-type results in dimension , and for radial solutions in any dimension. We also provide some partial results for non-radial solutions in dimension . Our proofs are based on a generalized Gidas-Spruck technique, combined with the idea of Serrin and Zou (Acta Math 189(1):79-142, 2002) and of Bidaut-V,ron (Aequations aux d,riv,es partielles et applications. Elsevier, Paris, pp 189-198, 1998). Finally, we clarify and correct some of the previous results on this topic.
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页码：519 / 537
页数：19
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