In this paper,we study the Radon measure initial value problem for the nonisentropic improved Aw-Rascle-Zhang model.For arbitrary convex F(u)in this model we construct the Riemann solutions by elementary waves andδ-s...In this paper,we study the Radon measure initial value problem for the nonisentropic improved Aw-Rascle-Zhang model.For arbitrary convex F(u)in this model we construct the Riemann solutions by elementary waves andδ-shock waves using the method of generalized characteristic analysis.We obtain the solutions constructively for initial data containing the Dirac measure by taking the limit of the solutions for that with three piecewise constants.Moreover,we analyze different kinds of wave interactions,including the interactions of theδ-shock waves with elementary waves.展开更多
This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for...This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for the propagation of wave profiles β ＋ mδ and β ＋ mδt are presented （β is a real continuous function, m ≠ 0 is a real number and δ＇ is the derivative of the Dirac measure 5）. These results are obtained with a consistent concept of solution based on our theory of distributional products. Burgers equation ut ＋ （u2/2）x = 0, the iffusionless Burgers-Fischer equation ut ＋ a（u2/2）x = ru（1 - u/k） with a, r, k being positive numbers, Leveque and Yee equation ut ＋ ux = μx（1 - u）（u - u/k） with μ ≠ 0, and some other examples are studied within such a setting. A ＂tool box＂ survey of the distributional products is also included for the sake of completeness.展开更多
基金supported by the Natural Science Foundation of Zhejiang(LQ18A010004)Matematical Analysis,The First class courses in Zhejiang Province(210052)+1 种基金the Fundamental Research Funds for the Provincial Universities of Zhejiang(210039)supported by the National Natural Science Foundation of China(11771442)。
文摘In this paper,we study the Radon measure initial value problem for the nonisentropic improved Aw-Rascle-Zhang model.For arbitrary convex F(u)in this model we construct the Riemann solutions by elementary waves andδ-shock waves using the method of generalized characteristic analysis.We obtain the solutions constructively for initial data containing the Dirac measure by taking the limit of the solutions for that with three piecewise constants.Moreover,we analyze different kinds of wave interactions,including the interactions of theδ-shock waves with elementary waves.
基金supported by Fundac ao para a Ci encia e a Tecnologia,PEst OE/MAT/UI0209/2011
文摘This paper contains a study of propagation of singular travelling waves u（x, t） for conservation laws ut ＋ [Ф（u）]x = ψ（u）, where Ф, ψ are entire functions taking real values on the real axis. Conditions for the propagation of wave profiles β ＋ mδ and β ＋ mδt are presented （β is a real continuous function, m ≠ 0 is a real number and δ＇ is the derivative of the Dirac measure 5）. These results are obtained with a consistent concept of solution based on our theory of distributional products. Burgers equation ut ＋ （u2/2）x = 0, the iffusionless Burgers-Fischer equation ut ＋ a（u2/2）x = ru（1 - u/k） with a, r, k being positive numbers, Leveque and Yee equation ut ＋ ux = μx（1 - u）（u - u/k） with μ ≠ 0, and some other examples are studied within such a setting. A ＂tool box＂ survey of the distributional products is also included for the sake of completeness.
