Stability of travelling wave solutions to a semilinear hyperbolic system with relaxation |
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Authors: | Yoshihiro Ueda |
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Affiliation: | Graduate School of Mathematics, Kyushu University, Hakozaki 6‐10‐1, Higashi‐ku, Fukuoka 812‐8581, Japan |
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Abstract: | We study a semilinear hyperbolic system with relaxation and investigate the asymptotic stability of travelling wave solutions with shock profile. It is shown that the travelling wave solution is asymptotically stable, provided the initial disturbance is suitably small. Moreover, we show that the time convergence rate is polynomially (resp. exponentially) fast as t→∞ if the initial disturbance decays polynomially (resp. exponentially) for x→∞. Our proofs are based on the space–time weighted energy method. Copyright © 2008 John Wiley & Sons, Ltd. |
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Keywords: | stability hyperbolic relaxation system damped wave equation with nonlinear convection weighted energy method convergence rate travelling wave |
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