On the dynamics of a strongly singular parabolic equation

In this paper we study the semiflow defined by a semilinear parabolic equation, in which both the diffusion and the reaction term present strong order of singularity at the origin. We justify the existence of a global branch of nontrivial equilibrium solutions for subcritical nonlinearities. The app...

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Bibliographic Details
Published in:Journal of mathematical analysis and applications 2015-01, Vol.421 (1), p.21-37
Main Authors: Trachanas, Georgios P., Zographopoulos, Nikolaos B.
Format: Article
Language:English
Subjects:
Global attractor
Global bifurcation
Singularities
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Summary:In this paper we study the semiflow defined by a semilinear parabolic equation, in which both the diffusion and the reaction term present strong order of singularity at the origin. We justify the existence of a global branch of nontrivial equilibrium solutions for subcritical nonlinearities. The approach, based on the critical Caffarelli–Kohn–Nirenberg inequality, follows the arguments of [21,22].
ISSN:0022-247X
1096-0813
DOI:10.1016/j.jmaa.2014.06.071