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This paper is mainly concerned with the formation of delta standing wave for the scalar conservation law with a linear flux function involving discontinuous coefficients by using the self-similar viscosity vanishing method. More precisely, we use the self-similar viscosity to smooth out the discontinuous coefficient such that the existence of approximate viscous solutions to the delta standing wave for the Riemann problem is established and then the convergence to the delta standing wave solution is also obtained when the viscosity parameter tends to zero. In addition, the Riemann problem is also solved with the standard method and the instability of Riemann solutions with respect to the specific small perturbation of initial data is pointed out in some particular situations.
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참고문헌 (38)
참고문헌 신청
M. Nedeljkov / 2010 / Shadow waves: entropies and interactions for delta and singular shocks / Arch. Ration. Mech. Anal 197(2):487~537
E. Yu. Panov / 2006 / δ′-shock waves as a new type of solutions to system of conservation laws / J. Differential Equations 228(1):49~86
C. Shen / 2012 / Structural stability of solutions to the Riemann problem for a scalar conser-vation law / J. Math. Anal. Appl 389(2):1105~1116
C. Shen / 2014 / On a regularization of a scalar conservation law with discontinuous coefficients / J. Math. Phys 55(3):031502
C. Shen / 2010 / Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model / J. Differential Equations 249(12):3024~3051
E. Yu. Panov / 2006 / δ′-shock waves as a new type of solutions to system of conservation laws / J. Differential Equations 228(1):49~86
C. Shen / 2012 / Structural stability of solutions to the Riemann problem for a scalar conser-vation law / J. Math. Anal. Appl 389(2):1105~1116
C. Shen / 2014 / On a regularization of a scalar conservation law with discontinuous coefficients / J. Math. Phys 55(3):031502
C. Shen / 2010 / Formation of delta shocks and vacuum states in the vanishing pressure limit of Riemann solutions to the perturbed Aw-Rascle model / J. Differential Equations 249(12):3024~3051
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