SAWTOOTH SOLUTIONS TO THE BURGERS EQUATION ON AN INTERVAL
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 the equation describes the movement in a dissipative medium, the initial profile of the solution will ev...
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| Main Authors: | , |
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| Format: | Article |
| Language: | Russian |
| Published: |
Moscow State Technical University of Civil Aviation
2016-11-01
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| Series: | Научный вестник МГТУ ГА |
| Subjects: | |
| Online Access: | https://avia.mstuca.ru/jour/article/view/601 |
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| Summary: | 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 the equation describes the movement in a dissipative medium, the initial profile of the solution will evolve to an time-invariant solution with the same boundary values. However there are three ways of obtaining the same result: the initial profile may regularly decay to the 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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| ISSN: | 2079-0619 2542-0119 |