In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of cl...In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.展开更多
By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomo...By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.展开更多
This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is st...This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.展开更多
文摘In this paper we investigate the formation of singularities of hyperbolic systems.Employing the method of parametric coordinates and the existence of the solution of the blow-up system, we prove that the blow-up of classic solutions is due to the envelope of characteristics of the same family, analyze the geometric properties of the envelope of characteristics and estimate the blowup rates of the solution precisely.
基金Project supported by Specialized Research Fund for the Doctoral Program of Higher Education.
文摘By means of the theory on the semi-global C^1 solution to the mixed initialboundary value problem （IBVP） for first order quasilinear hyperbolic systems, we establish the exact controllability for general nonautonomous first order quasilinear hyperbolic systems with general nonlinear boundary conditions.
基金Project supported by the Special Funds for Major State Basic Research Project of ChinaSpecialized Research Fund for the Doctoral Program of Higher Education (No. 20020246002).
文摘This paper deals with the blow-up phenomenon, particularly, the geometric blow-up mechanism, of classical solutions to the Cauchy problem for quasilinear hyperbolic systems in the critical case. We prove that it is still the envelope of the same family of characteristics which yields the blowup of classical solutions to the Cauchy problem in the critical case.
