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June 2005 Kuramoto-Sivashinsky type equations on a half-line
Felipe Benitez, Elena I. Kaikina
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SUT J. Math. 41(2): 153-178 (June 2005). DOI: 10.55937/sut/1159986966

Abstract

We study the initial-boundary value problem for a general class of nonlinear dissipative equations on a half-line

(0.1){ut+N(u,ux)+Ku=f,(x,t)R+×R+u(x,0)=u0(x),xR+,xj1u(0,t)=hj(t)forj=1,,M,

where the nonlinear term (u,ux) depends on the unknown function u and its derivative ux and satisfies the estimate

|(u,υ)|C|u|ρ|υ|σ

with ρ,σ 0 and the linear operator K(u) is defined as follows

K(u)=αnxn+αmxm,

where the constants αn, αmR, n,m are integers, m>n, nM + 1, n is an even integer.

The aim of this paper is to prove the global existence of solutions to the initial-boundary value problem (0.1). We find the main term of the asymptotic representation of solutions.

Funding Statement

This work is partially supported by CONACYT.

Acknowledgement

We are grateful to unknown referee for many useful suggestions and comments.

Citation

Download Citation

Felipe Benitez. Elena I. Kaikina. "Kuramoto-Sivashinsky type equations on a half-line." SUT J. Math. 41 (2) 153 - 178, June 2005. https://doi.org/10.55937/sut/1159986966

Information

Received: 4 August 2005; Published: June 2005
First available in Project Euclid: 18 June 2022

Digital Object Identifier: 10.55937/sut/1159986966

Subjects:
Primary: 35B40 , C35Q55

Keywords: Initial-boundary value problem , large time asymptotics , nonlinear dissipative equations

Rights: Copyright © 2005 Tokyo University of Science

Vol.41 • No. 2 • June 2005
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