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Behavior of Solutions of Burgers′ Equation with Nonlocal Boundary Conditions

✍ Scribed by K. Deng

Publisher
Elsevier Science
Year
1994
Tongue
English
Weight
684 KB
Volume
113
Category
Article
ISSN
0022-0396

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✦ Synopsis

In this paper, we discuss the long-time behavior of positive solutions of Burgers' equation (u_{t}=u_{x x}+\varepsilon u u_{x}, 00, t>0) with the nonlocal boundary condition: (u(0, t)=0, \quad u_{x}(1, t)+\frac{1}{2} \varepsilon u^{2}(1, t)=a u^{p}(1, t)\left(\int_{0}^{1} u(x, t) d x\right)^{q}), where (0<p<\infty), (0<q<\infty). Criteria for stability are given. Blowup in finite time for some solutions is shown. General results are discussed. 1994 Academic Press, Inc.

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