CENTER FOR COMPUTATIONAL MATHEMATICS COLLOQUIUM

                  UNIVERSITY OF COLORADO AT DENVER



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

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

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.