On the dynamics of a strongly singular parabolic equation

Georgios P. Trachanas; Nikolaos B. Zographopoulos

doi:10.1016/j.jmaa.2014.06.071

On the dynamics of a strongly singular parabolic equation

Georgios P. Trachanas
, Nikolaos B. Zographopoulos^*

^*Corresponding author for this work

School of Mathematics and Physics

National Technical University of Athens
Hellenic Army Academy

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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].

Original language	English
Pages (from-to)	21-37
Number of pages	17
Journal	Journal of Mathematical Analysis and Applications
Volume	421
Issue number	1
DOIs	https://doi.org/10.1016/j.jmaa.2014.06.071
Publication status	Published - 1 Jan 2015

Keywords

Global attractor
Global bifurcation
Singularities

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10.1016/j.jmaa.2014.06.071

Cite this

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title = "On the dynamics of a strongly singular parabolic equation",

abstract = "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].",

keywords = "Global attractor, Global bifurcation, Singularities",

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AU - Zographopoulos, Nikolaos B.

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N2 - 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].

AB - 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].

KW - Global attractor

KW - Global bifurcation

KW - Singularities

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JF - Journal of Mathematical Analysis and Applications

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On the dynamics of a strongly singular parabolic equation

Abstract

Keywords

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