In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbol...In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region.Under the generalized entropy conditions,we find that there are different shock wave structures for different parameters.To guarantee the uniqueness of the solutions,we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters.Finally,we construct the Riemann solutions in some solvable regions.展开更多
We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent devel...We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.展开更多
Detonation is initiated through a hot jet in a supersonic premixed mixture of H2 and air,which is produced by using a air heater.The results show that initiation fails in the low-equivalence-ratio premixed gas.With th...Detonation is initiated through a hot jet in a supersonic premixed mixture of H2 and air,which is produced by using a air heater.The results show that initiation fails in the low-equivalence-ratio premixed gas.With the increase of equivalence ratio,the hot jet can induce deflagration to detonation transition(DDT)in the premixed mixture,which an indirect initiation of detonation.Further studies show that the DDT process is due to the combined effect of a local hemispherical explosion shock wave,the bow shock,and the flame produced by the hot jet.展开更多
基金the National Natural Science Foundation of China(11771442)。
文摘In this paper,we study the shock waves for a mixed-type system from chemotaxis.We are concerned with the jump conditions for the left state which is located in the elliptical region and the right state in the hyperbolic region.Under the generalized entropy conditions,we find that there are different shock wave structures for different parameters.To guarantee the uniqueness of the solutions,we obtain the admissible shock waves which satisfy the generalized entropy condition in both parameters.Finally,we construct the Riemann solutions in some solvable regions.
基金The research of Gui-Qiang G.Chen was supported in part by the UK Engineering and Physical Sciences Research Council Awards EP/L015811/1,EP/V008854/1,EP/V051121/1the Royal Society-Wolfson Research Merit Award WM090014.
文摘We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.
基金the National Natural Science Foundation of China under Grant Nos 91016028,91016012 and 51006119.
文摘Detonation is initiated through a hot jet in a supersonic premixed mixture of H2 and air,which is produced by using a air heater.The results show that initiation fails in the low-equivalence-ratio premixed gas.With the increase of equivalence ratio,the hot jet can induce deflagration to detonation transition(DDT)in the premixed mixture,which an indirect initiation of detonation.Further studies show that the DDT process is due to the combined effect of a local hemispherical explosion shock wave,the bow shock,and the flame produced by the hot jet.
