Gradient catastrophes and sawtooth solutions for a generalized Burgers equation on an interval |
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Affiliation: | Department of Mathematics, Moscow State Technical University of Civil Aviation, 20 Kronshtadtsky blvd., Moscow, 125493, Russia |
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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. |
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Keywords: | Burger’s equation Initial value-boundary problem Gradient catastrophes Sawtooth solutions |
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