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Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation

Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order... We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed. Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Existence and asymptotic behavior of solution of Cauchy problem for the damped sixth-order Boussinesq equation

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Publisher
Springer Journals
Copyright
Copyright © 2015 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/s10255-012-0174-2
Publisher site
See Article on Publisher Site

Abstract

We consider the existence, both locally and globally in time, as well as the asymptotic behavior of solutions for the Cauchy problem of the sixth-order Boussinesq equation with damping term. Under rather mild conditions on the nonlinear term and initial data, we prove that the above-mentioned problem admits a unique local solution, which can be continued to a global solution, and the problem is globally well-posed. Finally, under certain conditions, we prove that the global solution decays exponentially to zero in the infinite time limit.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jun 16, 2012

References