In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-i...In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.展开更多
In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by...In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.展开更多
基金partially supported by NSFC(11871133,12171498)partially supported by NSFC(11971402,12171401)the NSF of Fujian province,China(2020J01029)。
文摘In this paper,we study the transonic shock solutions to the steady Euler system in a quasi-one-dimensional divergent-convergent nozzle.For a given physical supersonic inflow at the entrance,we obtain exactly two non-isentropic transonic shock solutions for the exit pressure lying in a suitable range.In addition,we establish the monotonicity between the location of the transonic shock and the pressure downstream.
基金supported by the National Natural Science Foundation of China(11361053,11201204,11471148,11471330,145RJZA112)
文摘In this article, we consider positive steady state solutions and dynamics for a spatially heterogeneous predator-prey system with modified Leslie-Gower and Holling-Type II schemes. The heterogeneity here is created by the degeneracy of the intra-specific pressures for the prey. By the bifurcation method, the degree theory, and a priori estimates, we discuss the existence and multiplicity of positive steady states. Moreover, by the comparison argument, we also discuss the dynamical behavior for the diffusive predator-prey system.
