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Volume 20, Issue 2
Asymptotic Behavior of Global Classical Solutions to a Kind of Mixed Initial-boundary Value Problem

Jiaguo Zhang

J. Part. Diff. Eq., 20 (2007), pp. 114-130.

Published online: 2007-05

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  • Abstract

We study the asymptotic behavior of global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Based on the existence results on the global classical solutions given by Li and Wang in [1] and employing the method of Kong and Yang in [2], we prove that, when t tends to infinity, the solution approaches a combination of C¹ travelling wave solutions at the algebraic rate (1+t)^{-μ}, provided that the initial data decay at the rate (1+x)^{-(1+μ)} as x tends to +∞ and the boundary data decay at the rate (1+t)^{-(1+μ)} as t tends to +∞, where μ is a positive constant.

  • Keywords

Quasilinear hyperbolic system Global classical solution Asymptotic behavior Weak linear degeneracy Normalized coordinates Travelling wave

  • AMS Subject Headings

37D99.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JPDE-20-114, author = {Jiaguo Zhang }, title = {Asymptotic Behavior of Global Classical Solutions to a Kind of Mixed Initial-boundary Value Problem}, journal = {Journal of Partial Differential Equations}, year = {2007}, volume = {20}, number = {2}, pages = {114--130}, abstract = {

We study the asymptotic behavior of global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Based on the existence results on the global classical solutions given by Li and Wang in [1] and employing the method of Kong and Yang in [2], we prove that, when t tends to infinity, the solution approaches a combination of C¹ travelling wave solutions at the algebraic rate (1+t)^{-μ}, provided that the initial data decay at the rate (1+x)^{-(1+μ)} as x tends to +∞ and the boundary data decay at the rate (1+t)^{-(1+μ)} as t tends to +∞, where μ is a positive constant.

}, issn = {2079-732X}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jpde/5297.html} }
TY - JOUR T1 - Asymptotic Behavior of Global Classical Solutions to a Kind of Mixed Initial-boundary Value Problem AU - Jiaguo Zhang JO - Journal of Partial Differential Equations VL - 2 SP - 114 EP - 130 PY - 2007 DA - 2007/05 SN - 20 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jpde/5297.html KW - Quasilinear hyperbolic system KW - Global classical solution KW - Asymptotic behavior KW - Weak linear degeneracy KW - Normalized coordinates KW - Travelling wave AB -

We study the asymptotic behavior of global classical solutions to a kind of mixed initial-boundary value problem for quasilinear hyperbolic systems. Based on the existence results on the global classical solutions given by Li and Wang in [1] and employing the method of Kong and Yang in [2], we prove that, when t tends to infinity, the solution approaches a combination of C¹ travelling wave solutions at the algebraic rate (1+t)^{-μ}, provided that the initial data decay at the rate (1+x)^{-(1+μ)} as x tends to +∞ and the boundary data decay at the rate (1+t)^{-(1+μ)} as t tends to +∞, where μ is a positive constant.

Jiaguo Zhang . (2007). Asymptotic Behavior of Global Classical Solutions to a Kind of Mixed Initial-boundary Value Problem. Journal of Partial Differential Equations. 20 (2). 114-130. doi:
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