On nonlinear reaction-diffusion systems
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TL;DR: In this article, a qualitative analysis for a coupled system of two reaction-diffusion equations under various boundary conditions which arises from a number of physical problems is presented, where the nonlinear reaction functions are classified into three basic types according to their relative quasi-monotone property.
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About: This article is published in Journal of Mathematical Analysis and Applications. The article was published on 01 May 1982. and is currently open access. The article focuses on the topics: Neumann boundary condition & Boundary value problem.
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Citations
Some uniqueness and exact multiplicity results for a predator-prey model
Yihong Du,Yuan Lou,Yuan Lou +2 more
TL;DR: In this article, the authors considered positive solutions of a predator-prey model with diffusion and under homogeneous Dirichlet boundary conditions, and obtained various results on the exact number of positive solutions.
S-Shaped Global Bifurcation Curve and Hopf Bifurcation of Positive Solutions to a Predator–Prey Model
Yihong Du,Yuan Lou +1 more
TL;DR: In this article, the authors studied the number of positive solutions of (1.0) and the stability of these solutions and showed that when b, d, c, and m fall into a certain range, the solution set (u, v, a) forms a S-shaped smooth curve, and that Hopf bifurcation occurs along this curve.
96
Global stability in a diffusive Holling-Tanner predator-prey model
TL;DR: It is proved that the unique constant equilibrium in the diffusive Holling–Tanner predator–prey model is globally asymptotically stable under a new simpler parameter condition.
86
Global well-posedness of coupled parabolic systems
TL;DR: In this article, the initial boundary value problem of a class of reaction-diffusion systems (coupled parabolic systems) with nonlinear coupled source terms is considered in order to classify the initial data for the global existence, finite time blowup and long time decay of the solution.
81
References
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Maximum principles in differential equations
Murray H. Protter,Hans F. Weinberger +1 more
- 01 Jan 1967
TL;DR: The One-Dimensional Maximum Principle (MDP) as mentioned in this paper is a generalization of the one-dimensional maximum principle (OMP) for the construction of hyperbolic equations.
3.8K
Oscillations in chemical systems. IV. Limit cycle behavior in a model of a real chemical reaction
TL;DR: In this paper, the authors generalized the chemical mechanism of Field, Koros, and Noyes for the oscillatory Belousov reaction by a model composed of five steps involving three independent chemical intermediates.
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