Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Long-time asymptotics of solutions of the third-order nonlinear evolution equation governing wave propagation in relaxing media

Author: Vladimir Varlamov
Journal: Quart. Appl. Math. 58 (2000), 201-218
MSC: Primary 35L80; Secondary 35B40
DOI: https://doi.org/10.1090/qam/1753395
MathSciNet review: MR1753395
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Abstract: A classical Cauchy problem for a third-order nonlinear evolution equation is considered. This equation describes the propagation of weakly nonlinear waves in relaxing media. The global existence and uniqueness of its solutions is proved and the solution is constructed in the form of a series in a small parameter present in the initial conditions. Its long-time asymptotics is calculated, which shows the presence of two solitary wave pulses traveling in opposite directions and diffusing in space. Each of them is governed by Burgers' equation with a transfer.

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DOI: https://doi.org/10.1090/qam/1753395
Article copyright: © Copyright 2000 American Mathematical Society

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