Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers' equation

Authors: Keng Deng, Man Kam Kwong and Howard A. Levine
Journal: Quart. Appl. Math. 50 (1992), 173-200
MSC: Primary 35Q53; Secondary 35B40, 76D05
DOI: https://doi.org/10.1090/qam/1146631
MathSciNet review: MR1146631
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Abstract: We study the long time behavior of solutions of Burgers's equation with nonlocal nonlinearities: $ {u_t} = {u_{xx}} + \varepsilon u{u_x} + \frac{1}{2}\left( {a\parallel u\left( ... ... - 1}} + b} \right)u, 0 < x < 1, \\ a, \varepsilon \in \mathbb{R}, b > 0, p > 1$, subject to $ u\left( {0, t} \right) = u\left( {1, t} \right) = 0$. A stability-instability analysis is given in some detail, and some finite time blow up results are given.

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DOI: https://doi.org/10.1090/qam/1146631
Article copyright: © Copyright 1992 American Mathematical Society

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