Perturbation of a shock wave

I. O. Rasskazov

Institute of Mathematics with Computing Centre, Ufa Science Centre, Russian Academy of Sciences

Abstract: The Cauchy problem is considered for the perturbed Hopf equation $u_t+uu_x=\varepsilon f(u)$, $\varepsilon\to0$. The solution in the continuity domain can be expanded in the standard asymptotic series in integral powers of the small parameter. An asymptotic representation is found for the line of propagation of the shock wave.

DOI: 10.4213/tmf719

 English version: Theoretical and Mathematical Physics, 1999, 118:3, 365–368

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