Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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



Behavior of solutions of Burgers's equation with nonlocal boundary conditions. II

Author: Keng Deng
Journal: Quart. Appl. Math. 52 (1994), 553-567
MSC: Primary 35Q53; Secondary 35B40, 35K60
DOI: https://doi.org/10.1090/qam/1292205
MathSciNet review: MR1292205
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Abstract: We study the large-time behavior of positive solutions of Burgers's equation $ {u_t} = {u_{xx}} + \varepsilon u{u_x}, 0 < x < 1, t > 0\left( {\varepsilon > 0} \right)$, subject to the nonlocal boundary condition: $ - {u_x}\left( {0, t} \right) - \frac{1}{2}\varepsilon {u^2}\left( {0, t} \righ... ...x} \right)^q},u\left( {1, t} \right) = 0 \\ \left( {0 < p, q < \infty } \right)$. The steady-state problem is analyzed in detail, and the result about finite-time blow-up is proved.

References [Enhancements On Off] (What's this?)

  • [1] K. Deng, Behavior of solutions of Burgers' equation with nonlocal boundary conditions (I), J. Differential Equations (to appear)
  • [2] K. Deng, M. K. Kwong, and H. A. Levine, The influence of nonlocal nonlinearities on the long time behavior of solutions of Burgers's equation, Quart. Appl. Math. 50, 173-200 (1992)
  • [3] H. A. Levine, Stability and instability for solutions of Burgers' equation with a semilinear boundary condition, SIAM J. Math. Anal. 19, 312-336 (1988)

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DOI: https://doi.org/10.1090/qam/1292205
Article copyright: © Copyright 1994 American Mathematical Society

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