Boundary and interior transition layer phenomena for pairs of second-order differential equations☆
Paul C. Fife,Paul C. Fife +1 more
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In this article, the authors considered a family of solutions with a limit in some sense as l + 0, where l is the number of vertices in the solution and E is the length of the transition from the limit to the boundary.About:
This article is published in Journal of Mathematical Analysis and Applications.The article was published on 1976-05-01 and is currently open access. It has received 145 citations till now. The article focuses on the topics: Boundary (topology).read more
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Asymptotic Behavior of Dissipative Systems
TL;DR: In this article, the authors consider a continuous dynamical system with a global attractor and describe the properties of the flow on the attractor asymptotically smooth and Morse-Smale maps.
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On a diffusive prey-predator model which exhibits patchiness
Masayasu Mimura,James D. Murray +1 more
TL;DR: It is shown that when the diffusion of the prey is small compared with that of the predator the non-linearity which is called a hump effect in the prey interaction, is a key mechanism for the system to exhibit, asymptotically in time, stable heterogeneity in a bounded domain with zero flux boundary conditions.
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On positive solutions of some pairs of differential equations
TL;DR: In this paper, it was shown that the existence and uniqueness of strictly positive solutions of the Conwat-Gardner-Smoller (CGS) equations can be proven by iteration and asymptotic methods.
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Travelling waves for delayed reaction–diffusion equations with global response
TL;DR: In this paper, the authors developed a new approach to obtain the existence of travelling wave solutions for reaction-diffusion equations with delayed non-local response, based on an abstract formulation of the wave profile as a solution of an operational equation in a certain Banach space, coupled with an index formula of the associated Fredholm operator.
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A picture of the global bifurcation diagram in ecological interacting and diffusing systems
TL;DR: In this paper, the authors present global phenomena of pattern formation in stationary reaction-diffusion equations, possessing Turing's diffusion-induced instability, which appear typically in mathematical biology, by integrating two complementary approaches-analytical and numerical.
References
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Partial Differential Equations
TL;DR: In this paper, the authors present a theory for linear PDEs: Sobolev spaces Second-order elliptic equations Linear evolution equations, Hamilton-Jacobi equations and systems of conservation laws.
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Interior Transition Layers for Elliptic Boundary Value Problems with a Small Parameter
P C Fife,W M Greenlee +1 more
TL;DR: In this article, the invertibility of a generalized implicit function theorem was shown to be invertible under the assumption that the implicit function is linear in the number of nodes.
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