Nonexistence results for the Cauchy problem for some fractional nonlinear systems of thermo-elasticity type

We study the nonexistence of global solutions to the Cauchy problem for systems of parabolic‐hyperbolic or hyperbolic thermo‐elasticity equations posed in RN. For power nonlinearities, we present threshold critical exponents depending on the space dimension N. Our method of proof rests on the nonlin...

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Bibliographic Details
Published in:Zeitschrift für angewandte Mathematik und Mechanik 2016-09, Vol.96 (9), p.1119-1128
Main Authors: Boutefnouchet, M., Erjaee, H., Kirane, M., Qafsaoui, M.
Format: Article
Language:English
Subjects:
35K22
35L52
35Q79
Cauchy problem
Cauchy problems
degenerate systems
Dynamical systems
Elasticity
Exponents
Mathematical analysis
Nonexistence of global solutions
Nonlinear dynamics
Nonlinearity
Rest
strongly coupled systems
threshold exponent
Thresholds
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Summary:We study the nonexistence of global solutions to the Cauchy problem for systems of parabolic‐hyperbolic or hyperbolic thermo‐elasticity equations posed in RN. For power nonlinearities, we present threshold critical exponents depending on the space dimension N. Our method of proof rests on the nonlinear capacity method. The authors study the nonexistence of global solutions to the Cauchy problem for systems of parabolic‐hyperbolic or hyperbolic thermo‐elasticity equations posed in RN. For power nonlinearities, we present threshold critical exponents depending on the space dimension N. Their method of proof rests on the nonlinear capacity method.
ISSN:0044-2267
1521-4001
DOI:10.1002/zamm.201500134