A Lyapunov functional and blow-up results for a class of perturbed semilinear wave equations

We consider in this paper some class of perturbation for the semilinear wave equation with subcritical (in the conformal transform sense) power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to derive the blow-up rate. Although the result is similar to th...

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Bibliographic Details
Published in:Nonlinearity 2012-09, Vol.25 (9), p.2759-2773
Main Authors: Hamza, M A, Zaag, H
Format: Article
Language:English
Subjects:
Analysis of PDEs
blow-up rate
Exact sciences and technology
finite time blow-up
Global analysis, analysis on manifolds
Mathematical analysis
Mathematical methods in physics
Mathematics
Nonlinearity
Other topics in mathematical methods in physics
Partial differential equations
Perturbation
perturbations
Physics
Sciences and techniques of general use
Similarity
Topology. Manifolds and cell complexes. Global analysis and analysis on manifolds
Transforms
Wave equation
Wave equations
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Summary:We consider in this paper some class of perturbation for the semilinear wave equation with subcritical (in the conformal transform sense) power nonlinearity. We first derive a Lyapunov functional in similarity variables and then use it to derive the blow-up rate. Although the result is similar to the unperturbed case in its statements, this is not the case of our method, which is new to our knowledge.
ISSN:0951-7715
1361-6544
DOI:10.1088/0951-7715/25/9/2759