Naslov
Singular solutions for the shallow water equations

Autori
Kalisch, Henrik ; Mitrović, Darko

Izvornik
Ima journal of applied mathematics (0272-4960) 77 (2012), 3; 340-350

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Shallow water equations; singular solutions

Sažetak
We construct singular solutions for the shallow water system. The method of weak asymptotics is used to find singular solutions of the shallow-water system which can contain Dirac-δ distributions (Espinosa & Omel'yanov, 2005). Complex-valued approximations which become real-valued in the distributional limit are shown to extend the range of possible singular solutions. It is shown, in this paper, how this approach can be used to construct solutions containing combinations of classical hyperbolic shock waves and Dirac-δ distributions. Uniqueness is obtained in a smaller class of distributions which satisfies a condition of Oleinik type and minimizes the number of δ-singularities.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

Napomena
Rad je prezentiran na skupu The IMA Conference on Nonlinearity and Coherent Structures.

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