Bifurcation of steady-state solutions of a scalar reaction-diffusion equation in one space variable

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...

Steady 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...

Generic Bifurcation of Steady-State Solutions

Brunovsky and Chow [ 1 ] have recently proved that for a generic C2 function with the Whitney topology, the “time map” r(.,f) (see [4]) associated with the differential equation U” +f(u) = 0 with homogeneous Dirichlet or Neumann boundary conditions, is a Morse function. In this note we give a simpler proof of this result as well as some new applications. Our method of proof is quite elementary,...

Travelling Wave Solutions of the One Dimensional Diffusion-reaction Equation

Solutions of diffusion equation for point defects

An analytical solution of the equation describing diffusion of intrinsic point defects in semiconductor crystals has been obtained for a one-dimensional finite-length domain with the Robin-type boundary conditions. The distributions of point defects for different migration lengths of defects have been calculated. The exact analytical solution was used to verify the approximate numerical solutio...