Year: 2008
Journal of Partial Differential Equations, Vol. 21 (2008), Iss. 2 : pp. 173–192
Abstract
We consider the asymptotic behavior of solutions to a model of hyperbolic- elliptic coupled system on the half-line R_+ = (0,∞), u_t+uu_x+q_x=0, -q_{xx}+q+u_x=0, with the Dirichlet boundary condition u(0, t) = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58(2004), 211-250] have shown that the solution to the correspond- ing Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_-< u_+. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution (u, q) is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L^2-energy method and L^1-estimate. It decays much lower than that of the corresponding Cauchy problem.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/2008-JPDE-5276
Journal of Partial Differential Equations, Vol. 21 (2008), Iss. 2 : pp. 173–192
Published online: 2008-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 20
Keywords: Hyperbolic-elliptic coupled system