Gene A. Klaasen

Stationary wave solutions of a system of reaction-diffusion equations derived from the Fitzhugh-Nagumo equations

We consider an extension of the FitzHugh–Nagumo model, namely the system \[ u_t = D_1 u_{xx} + f(u) - w,\qquad w_t = D_2 w_{xx} + \varepsilon (u - \gamma w) \] where

The Stability of Traveling Wave Front Solutions of a Reaction-Diffusion System

\varepsilon > 0,\gamma > 0,D_1 > 0,D_2 > 0

Continuous Dependence for N Boundary Value Problems

and

The existence, uniqueness, and instability of spherically symmetric solutions of a system of reaction—Diffusion equations

f(u)

Differential inequalities and existence theorems for second and third order boundary value problems

is cubic. We allow

A Variation of the Topological Method of Ważewski

\gamma

Local Uniqueness and Existence of Solutions of a Three-Point Boundary Value Problem

to be large which implies that there are three constant solutions. We show that over an appropriate range of parameters the system has time independent pulse solutions and an infinite number of periodic solutions. Depending on the particular choice of parameters, we show that the pulse solution leads to either the first constant solution or the third constant solution.

Stationary spatial patterns for a reaction-diffusion system with an excitable steady state

We investigate the behavior of solutions of the problem\[\begin{gathered} \frac{{\partial x}} {{\partial t}} = F( x,y ) + \frac{{D\partial ^2x }} {{\partial \zeta ^2 }},\quad \frac{{\partial y}} {{...

Dominance of N-th order linear equations

Consider the Nth order differential equation

On the Disconjugate Behavior of

( 1 )\qquad y^{( N )} = f\left( {t,y,y^1 , \cdots ,y^{( {N - 1} )} } \right)