Dynamic transitions of generalized Burgers equation. (English) Zbl 1333.35203
Summary: In this article, we study the dynamic transition for the one dimensional generalized Burgers equation with periodic boundary condition. The types of transition are dictated by the sign of an explicitly given parameter \(b\), which is derived using the dynamic transition theory developed by T. Ma and S. Wang [Phase transition dynamics. New York, NY: Springer (2014; Zbl 1285.82004)]. The rigorous result demonstrates clearly the types of dynamics transition in terms of length scale \(l\), dispersive parameter \(\delta\) and viscosity \(\nu\).
MSC:
| 35Q35 | PDEs in connection with fluid mechanics |
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
Keywords:
generalized Burgers equation; centre manifold reduction; phase transition dynamics; spatial-temporal patternsCitations:
Zbl 1285.82004References:
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