Abstract
In this chapter, we study the initial value problem of Burgers equation on the entire real line. The unknown of the Burgers equation models the first order elevation of the free surface of viscous fluid flow down an inclined plate. The Cole-Hopf transform can convert the nonlinear Burgers equation into a linear heat equation. Hence the initial value problem for the Burgers equation can be solved analytically. Analytic solutions to the Burgers equation for two different initial conditions are found. These solutions are the Burgers shock waves and the triangular waves respectively. The Burgers shock waves have a jump discontinuity when the viscosity approaches zero and they are stable. This stability claim will be proved in section 5.3. But the triangular wave is not stable and is only a transient state.
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References
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© 1993 Springer Science+Business Media Dordrecht
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Shen, S.S. (1993). Burgers Equation. In: A Course on Nonlinear Waves. Nonlinear Topics in the Mathematical Sciences, vol 3. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2102-6_5
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DOI: https://doi.org/10.1007/978-94-011-2102-6_5
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-4932-0
Online ISBN: 978-94-011-2102-6
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