Singular solutions for 2x2 systems in nonconservative form with incomplete set of eigenvectors

Electronic Journal of Differential Equations

关键词: Hyperbolic systems of conservation laws;    delta-shock wave type solution;    weak asymptotic method;   

DOI  :  

来源: DOAJ

【 摘 要 】

In this article, we study the initial-value problem for two first-ordersystems in non-conservative form. The first system arises in elastodynamicsand belongs to the class of strictly hyperbolic, genuinely nonlinear systems.The second system has repeated eigenvalues and an incomplete set of righteigenvectors. Solutions to such systems are expected to develop singularconcentrations. Existence of singular solutions to both the systems havebeen shown using the method of weak asymptotics. The second system hasbeen shown to develop singular concentrations even from Riemann-type initialdata. The first system differing from the second in having an extra termcontaining a positive constant k, the solution constructed for thefirst system have been shown to converge to the solution of the second ask tends to 0.

【 授权许可】

Unknown