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Interactions of delta shock waves for the transport equations with split delta functions. (English) Zbl 1159.35042

Summary: This paper is concerned with the interactions of \(\delta \)-shock waves and the vacuum states between the two contact discontinuities for the transport equations. The solutions are obtained constructively when the initial data are three piecewise constant states. The global structure and large time-asymptotic behaviors of the solutions are analyzed case by case. Moreover, it can be found that the Riemann solutions are stable for such small perturbations with initial data by studying the limits of the solutions when the perturbed parameter \(\varepsilon \) tends to zero.

MSC:

35L67 Shocks and singularities for hyperbolic equations
35B40 Asymptotic behavior of solutions to PDEs
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