STABILITY ANALYSIS FOR A FAMILY OF DEGENERATE SEMILINEAR PARABOLIC PROBLEMS CHARLES

被引：3
|
作者：
Stuart, Charles A. [1 ]
机构：
[1] Ecole Polytech Fed Lausanne, Dept Math, Stn 8, CH-1015 Lausanne, Switzerland
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2018年 / 38卷 / 10期
关键词：
Stability; instability; Lyapunov function; degenerate parabolic; KOHN-NIRENBERG INEQUALITIES; WEIGHTED SOBOLEV SPACES; BOUNDARY-VALUE PROBLEM; ELLIPTIC-EQUATIONS; BIFURCATION POINTS; HARNACK INEQUALITY; EXTREMAL-FUNCTIONS; EXISTENCE; NONEXISTENCE; EMBEDDINGS;
D O I：
10.3934/dcds.2018234
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
This paper deals with the initial value problem for a class of degenerate nonlinear parabolic equations on a bounded domain in R-N for N >= 2 with the Dirichlet boundary condition. The assumptions ensure that u (math) 0 is a stationary solution and its stability is analysed. Amongst other things the results show that, in the case of critical degeneracy, the principle of linearized stability fails for some simple smooth nonlinearities. It is also shown that for levels of degeneracy less than the critical one linearized stability is justified for a broad class of nonlinearities including those for which it fails in the critical case.
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页码：5297 / 5337
页数：41
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