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Kwon, Bongsuk
Partial Differential Equations and their applications
Research Interests
  • Partial differential equations, hyperbolic conservation laws, stability of nonlinear waves

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

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Title
Large-time behavior of solutions to an outflow problem for a shallow water model
Author
Kwon, BongsukSuzuki, MasahiroTakayama, Masahiro
Keywords
HYPERBOLIC CONSERVATION-LAWS; BOUNDARY VALUE-PROBLEMS; HALF-SPACE; RELAXATION; EQUATIONS
Issue Date
201310
Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
Citation
JOURNAL OF DIFFERENTIAL EQUATIONS, v.255, no.7, pp.1883 - 1904
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.
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DOI
http://dx.doi.org/10.1016/j.jde.2013.05.025
ISSN
0022-0396
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