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2007 Large time asymptotics for the Ott-Sudan-Ostrovskiy type equations on a segment
Elena I. Kaikina
Differential Integral Equations 20(12): 1363-1388 (2007).

Abstract

We study the initial-boundary value problems for the nonlinear nonlocal equation on a segment $\left( 0,a\right) $ \begin{equation} \left\{ \begin{array}{c} u_{t}+\lambda \left\vert u\right\vert \text{ }u+C_{1}\int_{0}^{x}\frac{ u_{ss}(s,t)}{\sqrt{x-s}}ds=0,\text{ }t>0, \\ u(x,0)=u_{0}(x), \\ u(a,t)=h_{1}(t),u_{x}(0,t)=h_{2}(t),t>0, \end{array} \right. \label{2} \end{equation} where $\lambda \in \mathbf{R}$ and the constant $C_{1}$ is chosen by the condition of the dissipation, such that $ {\rm Re\,}C_{1}p^{\frac{3}{2}}>0$ for ${\rm Re\,}p=0.$ The aim of this paper is to prove the global existence of solutions to the initial-boundary value problem and to find the main term of the asymptotic representation of solutions.

Citation

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Elena I. Kaikina. "Large time asymptotics for the Ott-Sudan-Ostrovskiy type equations on a segment." Differential Integral Equations 20 (12) 1363 - 1388, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35213
MathSciNet: MR2377022

Subjects:
Primary: 35K55
Secondary: 35B40 , 35C20 , 35K20

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 12 • 2007
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