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Start Over Descriptor "sawtooth solutions" Topic boundary value problems
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1. Gradient catastrophes and sawtooth solutions for a generalized Burgers equation on an interval.

Author

Samokhin, Alexey

Subjects
*CATASTROPHES (Mathematics), *DERIVATIVES (Mathematics), *BURGERS' equation, *INTERVAL analysis, *BOUNDARY value problems, *ASYMPTOTIC expansions, *LIMIT theorems
Abstract

The asymptotic behavior of solutions of the Burgers equation and its generalizations with initial value-boundary problem on a finite interval with constant boundary conditions is studied. Since it describes a dissipative medium, any initial profile will evolve to a time-invariant solution with the same boundary values. Yet there are three distinctive asymptotic processes: the initial profile may regularly decay to a smooth invariant solution; or a Heaviside-type gap develops through a dispersive shock and multi-oscillations; or an asymptotic limit is a stationary ‘sawtooth’ solution with periodical breaks of derivative. [ABSTRACT FROM AUTHOR]

Published
2014
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