Behaviors of Solutions for the Burgers Equation with Boundary corresponding to Rarefaction Waves
β Scribed by Liu, Tai-Ping; Matsumura, Akitaka; Nishihara, Kenji
- Book ID
- 118200190
- Publisher
- Society for Industrial and Applied Mathematics
- Year
- 1998
- Tongue
- English
- Weight
- 815 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0036-1410
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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)^
It is well known that Burgers' equation for plane waves can be transformed into the linear heat conduction equation yielding a general solution for any driving waveform on the boundary. Of especial current interest is the extent to which the difference-frequency signal can be "pumped" when the prima