Positive Steady-State Solutions of a Competing Reaction-Diffusion System with Large Cross-Diffusion Coefficients
نویسندگان
چکیده
منابع مشابه
Steady State Solutions of a Reaction-diffusion System Modeling Chemotaxis
We study the following nonlinear elliptic equation 8 < : u ? u + (e u R e u ? 1 jj) = 0 in ; @u @ = 0 on @; where is a smooth bounded domain in R 2. This equation arises in the study of stationary solutions of a chemotaxis system proposed by Keller and Segel. Under the condition that > jj ? 1 ; 6 = 4m for m = 1; 2; :::, where 1 is the rst (nonzero) eigenvalue of ? under the Neumann boundary con...
متن کاملSteady state coexistence solutions of reaction-diffusion competition models
Two species of animals are competing in the same environment. Under what conditions do they coexist peacefully? Or under what conditions does either one of the two species become extinct, that is, is either one of the two species excluded by the other? It is natural to say that they can coexist peacefully if their rates of reproduction and self-limitation are relatively larger than those of com...
متن کاملExistence of positive stationary solutions for a reaction-diffusion system
where λ > –π, α > are constants. By a positive solution, we mean a pair of functions (u,φ) with u,φ ∈ C(, ) ∩ C[, ] is a positive solution of (), if (u,φ) satisfies (), and u,φ ≥ , t ∈ [, ], u,φ ≡ . During the last few decades, concerning local equations, the question of the existence of solutions is one of the important topics, and it therefore has attracted much attention [–]....
متن کاملAn existence results on positive solutions for a reaction-diffusion model with logistics growth and indefinite weight
In this paper, using sub-supersolution argument, we prove an existence result on positive solution for an ecological model under certain conditions. It also describes the dynamics of the fish population with natural predation and constant yield harvesting. The assumptions are that the ecosystem is spatially homogeneous and the herbivore density is a constant which are valid assumptions for mana...
متن کاملModeling and Simulating Reaction-Diffusion Systems with State-Dependent Diffusion Coefficients
The present models and simulation algorithms of intracellular stochastic kinetics are usually based on the premise that diffusion is so fast that the concentrations of all the involved species are homogeneous in space. However, recents experimental measurements of intracellular diffusion constants indicate that the assumption of a homogeneous well-stirred cytosol is not necessarily valid even f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Analysis and Applications
سال: 1996
ISSN: 0022-247X
DOI: 10.1006/jmaa.1996.0039