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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    Title :

    SAWTOOTH SOLUTIONS TO THE BURGERS EQUATION ON AN INTERVAL


    Contributors:


    Publication date :

    2016



    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    Unknown





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