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Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations

Title	Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations
Author	Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.
Publication Date:	2014-01
Publication Place	- Elsevier
Subject	Nonlocal Cauchy problem, Global existence, Blow-up, Potential well, Boussinesq equation, Double dispersion equation
Type	Periodical
Language	English
Digital	Yes
Manuscript	No
Library:	Özyeğin University
Library Asset ID	0362-546X
Record ID	40f4b91b-ec22-4068-a2f4-6a6902cab608
Library Location	Natural and Mathematical Sciences
Date	2014-01
Notes	TÜBİTAK
Sample Text	In this paper we study the global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, View the MathML source, where the nonlocality enters through two pseudo-differential operators L and B. We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. Our results improve the global existence and blow-up results given in the literature for the present class of nonlocal nonlinear wave equations and cover those given for many well-known nonlinear dispersive wave equations such as the so-called double-dispersion equation and the traditional Boussinesq-type equations, as special cases.
DOI	10.1016/j.na.2013.09.013
Cilt	94

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Thresholds for global existence and blow-up in a general class of doubly dispersive nonlocal wave equations

Author Erbay, Hüsnü Ata, Erbay, Saadet, Erkip, A.

Publication Date 2014-01

Publication Place - Elsevier

Subject Nonlocal Cauchy problem, Global existence, Blow-up, Potential well, Boussinesq equation, Double dispersion equation

Type Periodical

Language English

Digital Yes

Manuscript No

Library Özyeğin University

Library Asset ID 0362-546X

Record ID 40f4b91b-ec22-4068-a2f4-6a6902cab608

Library Location Natural and Mathematical Sciences

Date 2014-01

Notes TÜBİTAK

Sample Text In this paper we study the global existence and blow-up of solutions for a general class of nonlocal nonlinear wave equations with power-type nonlinearities, View the MathML source, where the nonlocality enters through two pseudo-differential operators L and B. We establish thresholds for global existence versus blow-up using the potential well method which relies essentially on the ideas suggested by Payne and Sattinger. Our results improve the global existence and blow-up results given in the literature for the present class of nonlocal nonlinear wave equations and cover those given for many well-known nonlinear dispersive wave equations such as the so-called double-dispersion equation and the traditional Boussinesq-type equations, as special cases.

DOI 10.1016/j.na.2013.09.013

Cilt 94