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Blow up for the Wave Equation with a Fractional Damping
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M. R. Alaimia
Published/Copyright:
June 9, 2010
Abstract
We consider the wave equation with a fractional damping of order between 0 and 1 and a polynomial source. Introducing a new functional and using an argument due to Georgiev and Todorova [J. Differential Equations 109: 295–308, 1994] together with some appropriate estimates, it is proved that some solutions blow up in finite time.
Key words and phrases.: Blow up; Caputo's fractional derivative; integro-differential problem; modified energy functional; singular kernel
Received: 2003-09-22
Revised: 2004-07-28
Published Online: 2010-06-09
Published in Print: 2005-June
© Heldermann Verlag
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Keywords for this article
Blow up;
Caputo's fractional derivative;
integro-differential problem;
modified energy functional;
singular kernel
Articles in the same Issue
- On Nicely Definable Forcing Notions
- Sufficiency and Duality in Multiobjective Programming with Generalized (F, ρ)-Convexity
- A Generalized Upper and Lower Solution Method for Singular Discrete Boundary Value Problems for the One-Dimensional p-Laplacian
- Separately Nowhere Constant Functions; n-Cube and α-Prism Densities
- The Notion of V-r-Invexity in Differentiable Multiobjective Programming
- Existence for Some Quasilinear Elliptic Systems with Critical Growth Nonlinearity and L1 Data
- Solutions of Nonlinear Singular Boundary Value Problems
- Orthogonal Bases for Spaces of Complex Spherical Harmonics
- Blow up for the Wave Equation with a Fractional Damping
- Hadamard Product of Certain Classes of Functions
