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THE EXISTENCE OF A BOUNDED INVARIANT REGION FOR COMPRESSIBLE EULER EQUATIONS IN DIFFERENT GAS STATES
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作者 Weifeng JIANG Zhen WANG 《Acta Mathematica Scientia》 SCIE CSCD 2020年第5期1229-1239,共11页
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
关键词 Euler equations gas dynamic non-isentropic existence of invariant region
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Global Attractor of a Reaction-diffusion System with Hamiltonian Structure 被引量:1
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作者 黄建华 《Chinese Quarterly Journal of Mathematics》 CSCD 2001年第1期33-37,共5页
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
关键词 invariant region absorbing sets global attractor
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Global Bounded Solutions for Reaction-diffusion Systems with a Full Matrix of Diffusion Coefficients and a Balance Law
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作者 CHENXue-hong JIANGCheng-shun 《Chinese Quarterly Journal of Mathematics》 CSCD 2004年第1期16-23,共8页
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
关键词 Reaction diffusion systems invariant regions Lyapunov functional Global existence.
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Positivity-Preserving Numerical Methods for Belousov-Zhabotinsky Reaction
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作者 Yuro Adachi Novrianti Okihiro Sawada 《Applied Mathematics》 2020年第10期943-950,共8页
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
关键词 Positive Solution Difference Equation Belousov-Zhabotinsky Reaction invariant region Maximum Principle
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AN EXAMPLE OF PDE WITH TWO ATTRACTORS
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作者 王冠香 徐振源 刘曾荣 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1995年第9期833-838,共6页
A system of reaction-diffusion equations wity two attractors is given in this paper.The construction of the attractors is discussed.
关键词 invariant region. attractor. Hopf bifurcatior.
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GLOBAL ATTRACTOR OF A SPATIALLY DISCRETIZED REACTION-DIFFUSION SYSTEM WITH HAMILTONIAN STRUCTURE 被引量:1
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作者 黄建华 路钢 《Annals of Differential Equations》 1998年第2期87-97,共11页
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.
关键词 invariant region absorbing set global attractor.
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Relaxation Limit for Aw-Rascle System
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作者 DE LA CRUZ GUERRERO Richard A JUAJIBIOY Juan C RENDON Leonardo 《Journal of Partial Differential Equations》 2014年第2期166-175,共10页
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
关键词 Aw-Rascle system relaxation term compensated compactness invariant regions.
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