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On The Uniqueness of Solutions for Kawahara Type Equations

Part of: Equations of mathematical physics and other areas of application Partial differential equations

Published online by Cambridge University Press:  10 April 2018

Marcos A. de Farias ,
Cezar I. Kondo  and
José Ruidival dos Santos Filho
Marcos A. de Farias
Affiliation:
Universidade Federal de São Carlos PO Box 676, 13565-905, São Carlos-SP, Brazil (dcik@dm.ufscar.br; marcspbo@gmail.com; santos@dm.ufscar.br)
Cezar I. Kondo*
Affiliation:
Universidade Federal de São Carlos PO Box 676, 13565-905, São Carlos-SP, Brazil (dcik@dm.ufscar.br; marcspbo@gmail.com; santos@dm.ufscar.br)
José Ruidival dos Santos Filho
Affiliation:
Universidade Federal de São Carlos PO Box 676, 13565-905, São Carlos-SP, Brazil (dcik@dm.ufscar.br; marcspbo@gmail.com; santos@dm.ufscar.br)
*
*Corresponding author.
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Abstract

In this paper we extend to Kawahara type equations a uniqueness result obtained by C. E. Kenig, G. Ponce, and L. Vega for KdV type equations. We prove that, under certain decay's conditions, the null solution is the unique solution.

Keywords

Kawahara type equationsKdV type equationsuniqueness problems

MSC classification

Primary: 35A02: Uniqueness problems
Secondary: 35Q53: KdV-like equations (Korteweg-de Vries) 35Q35: PDEs in connection with fluid mechanics
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 61 , Issue 3 , August 2018 , pp. 623 - 646
Copyright
Copyright © Edinburgh Mathematical Society 2018 

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