In this article,by the mean-integral of the conserved quantity,we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region.Moreover,we obtain ...In this article,by the mean-integral of the conserved quantity,we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region.Moreover,we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process.Finally,we provide a mat hematical example showing that with a special state equation,a bounded invariant region for the non-isentropic process may exist.展开更多
In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets ...In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets and global attractor.展开更多
This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniqu...This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.展开更多
The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ens...The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.展开更多
In this paper, we discretize the Hénon-Heiles Hamiltonian system with Dirichlet boundary condition via spatial variable, and prove the existence of absorbing sets and global attractor of discrete system.
We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particul...We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particular Aw-Rascle system with source, where the source is the relaxation term, and we show the convergence of this solutions to the equilibrium state.展开更多
基金supported by the Natural Science Foundation of Zhejiang(LQ18A010004)the second author was supported by the Fundamental Research Funds for the Central Universities(WUT:2020IB011).
文摘In this article,by the mean-integral of the conserved quantity,we prove that the one-dimensional non-isentropic gas dynamic equations in an ideal gas state do not possess a bounded invariant region.Moreover,we obtain a necessary condition on the state equations for the existence of an invariant region for a non-isentropic process.Finally,we provide a mat hematical example showing that with a special state equation,a bounded invariant region for the non-isentropic process may exist.
文摘In this paper, we consider a reaction diffusion system with Hamitonian structure, we first prove the existence of an invariant region for system and the continuity of the semigroup, then establish the absorbing sets and global attractor.
基金Supported by the Henan Innovation Project for University Prominent Research Talents (2003KJCX008)
文摘This paper deals with an initial boundary value problem for the strongly coupledreaction-diffusion systems with a full matrix of diffusion coefficients. The global existence ofsolutions is proved by using the techniques based on invariant regions, Lyapunov functionalmethods, and local Lp prior estimates independent of time.
文摘The existence of positive solutions to the system of ordinary differential equations related to the Belousov-Zhabotinsky reaction is established. The key idea is to use a new successive approximation of solutions, ensuring its positivity. To obtain the positivity and invariant region for numerical solutions, the system is discretized as difference equations of explicit form, employing operator splitting methods with linear stability conditions. Algorithm to solve the alternate solution is given.
文摘In this paper, we discretize the Hénon-Heiles Hamiltonian system with Dirichlet boundary condition via spatial variable, and prove the existence of absorbing sets and global attractor of discrete system.
文摘We study the relaxation limit for the Aw-Rascle system of traffic flow. For this we apply the theory of invariant regions and the compensated compactness method to get global existence of Cauchy problem for a particular Aw-Rascle system with source, where the source is the relaxation term, and we show the convergence of this solutions to the equilibrium state.
