CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

TITLE:   Traveling Wave Solutions for Spatially Discrete Bistable
Reaction-Diffusion Equations

SPEAKER: Erik S. Van Vleck, Department of Mathematical and Computer Sciences,

DATE:    Wednesday, October 4, 1995

PLACE:   Math Conference Room - Suite 540
UCD Building, 1250 14th St., Denver

TIME:    2:30 pm (Refreshments served at 2:15 pm)

ABSTRACT

We consider traveling wave solutions of reaction-diffusion
equations on a discrete spatial domain. Traveling wave
equations are derived for the spatial domain, $\ZZ^n$
for $n=1,2,3$. Using an idealized nonlinear term, the
anisotropy introduced by the lattice is analyzed. In
particular, for $n=2$ we obtain traveling wave solutions
in various directions $e^{i\theta}$, and we explore the
relationship between the wave speed $c$, the angle
$\theta$, and the detuning parameter $a$ of the
nonlinearity. Of particular interest is the phenomenon
of propagation failure,'' and we compare and contrast
this phenomenon dependent upon whether the slope,
$\tan\theta$, is rational or irrational. Numerical
techniques for solving the traveling wave equations
are introduced. Finally, some numerical experiments
are presented.