Large-time behavior of solutions to an outflow problem for a shallow water model

Bongsuk Kwon, Masahiro Suzuki, Masahiro Takayama

Research output: Contribution to journalArticle

6 Citations (Scopus)

Abstract

We investigate the existence and the time-asymptotic stability of boundary layer solutions for a one-dimensional shallow water model. Under the subsonic condition on the far-field equilibrium state, we show that there exists a one-parameter family of boundary layer solutions satisfying the outflow constant-flux boundary condition. We also show that there is a unique time-asymptotic boundary layer profile for a given initial data, and prove its stability using standard energy methods, provided that the initial perturbation is sufficiently small. Our stability result is obtained without the zero mass condition nor "artificial" condition on the profile strength. Rather the time-asymptotic profile is determined alone by the initial perturbation from the end state so that it satisfies the zero mass condition and its amplitude is appropriately small simultaneously.

Original languageEnglish
Pages (from-to)1883-1904
Number of pages22
JournalJournal of Differential Equations
Volume255
Issue number7
DOIs
Publication statusPublished - 2013 Oct 1

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Large Time Behavior
Shallow Water
Behavior of Solutions
Boundary layers
Boundary Layer
Water
Asymptotic stability
Asymptotic Profile
Perturbation
Energy Method
Zero
Far Field
Equilibrium State
Boundary conditions
Model
Asymptotic Stability
Fluxes
Profile

ASJC Scopus subject areas

  • Analysis

Cite this

Large-time behavior of solutions to an outflow problem for a shallow water model. / Kwon, Bongsuk; Suzuki, Masahiro; Takayama, Masahiro.

In: Journal of Differential Equations, Vol. 255, No. 7, 01.10.2013, p. 1883-1904.

Research output: Contribution to journalArticle

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