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Omel’yanov, G. 2016. Propagation and interaction of solitons for nonintegrable equations. Russian Journal of Mathematical Physics, Vol. 23, Issue. 2, p. 225.
Omel’yanov, Georgy A. 2016. Modern Mathematical Methods and High Performance Computing in Science and Technology.
Shen, Chun 2016. The Riemann problem for the Chaplygin gas equations with a source term. ZAMM  Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 96, Issue. 6, p. 681.
Sun, Meina 2016. The exact Riemann solutions to the generalized Chaplygin gas equations with friction. Communications in Nonlinear Science and Numerical Simulation, Vol. 36, p. 342.
Tsikkou, Charis 2016. Singular shocks in a chromatography model. Journal of Mathematical Analysis and Applications, Vol. 439, Issue. 2, p. 766.
Kalisch, Henrik Mitrovic, Darko and Nordbotten, Jan M. 2015. Nonstandard shocks in the Buckley–Leverett equation. Journal of Mathematical Analysis and Applications, Vol. 428, Issue. 2, p. 882.
LI, XIUMEI and SHEN, CHUN 2015. THE DELTA STANDING WAVE SOLUTION FOR THE LINEAR SCALAR CONSERVATION LAW WITH DISCONTINUOUS COEFFICIENTS USING A SELFSIMILAR VISCOUS REGULARIZATION. Bulletin of the Korean Mathematical Society, Vol. 52, Issue. 6, p. 1945.
Omel'yanov, Georgy A. 2015. Solitontype asymptotics for nonintegrable equations: a survey. Mathematical Methods in the Applied Sciences, Vol. 38, Issue. 10, p. 2062.
Sarrico, C. O. R. 2015. The Riemann problem for the Brio system: a solution containing a Dirac mass obtained via a distributional product. Russian Journal of Mathematical Physics, Vol. 22, Issue. 4, p. 518.
Shen, Chun 2015. The Riemann problem for the pressureless Euler system with the Coulomblike friction term. IMA Journal of Applied Mathematics, p. hxv028.
Shen, Chun 2015. The Asymptotic Behaviors of Solutions to the Perturbed Riemann Problem near the Singular Curve for the Chromatography System. Journal of Nonlinear Mathematical Physics, Vol. 22, Issue. 1, p. 76.
Li, Xiumei and Shen, Chun 2013. Viscous Regularization of Delta Shock Wave Solution for a Simplified Chromatography System. Abstract and Applied Analysis, Vol. 2013, p. 1.
Sun, Meina 2013. Interactions of delta shock waves for the chromatography equations. Applied Mathematics Letters, Vol. 26, Issue. 6, p. 631.
Yin, Gan and Song, Kyungwoo 2013. Limits of Riemann Solutions to the Relativistic Euler Systems for Chaplygin Gas as Pressure Vanishes. Abstract and Applied Analysis, Vol. 2013, p. 1.
Existence and admissibility of δshock solutions is discussed for the nonconvex strictly hyperbolic system of equations
The system is fully nonlinear, i.e. it is nonlinear with respect to both unknowns, and it does not admit the classical Laxadmissible solution for certain Riemann problems. By introducing complexvalued corrections in the framework of the weak asymptotic method, we show that a compressive δshock solution resolves such Riemann problems. By letting the approximation parameter tend to zero, the corrections become real valued, and the solutions can be seen to fit into the framework of weak singular solutions defined by Danilov and Shelkovich. Indeed, in this context, we can show that every 2 × 2 system of conservation laws admits δshock solutions.
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