Minimum wave speeds in monostable reaction-diffusion equations: sharp bounds by polynomial optimization.

ABSTRACT: Many monostable reaction-diffusion equations admit one-dimensional travelling waves if and only if the wave speed is sufficiently high. The values of these minimum wave speeds are not known exactly, except in a few simple cases. We present methods for finding upper and lower bounds on minimum wave speed. They rely on constructing trapping boundaries for dynamical systems whose heteroclinic connections correspond to the travelling waves. Simple versions of this approach can be carried out analytically but often give overly conservative bounds on minimum wave speed. When the reaction-diffusion equations being studied have polynomial nonlinearities, our approach can be implemented computationally using polynomial optimization. For scalar reaction-diffusion equations, we present a general meth

SUBMITTER: Bramburger JJ 

PROVIDER: S-EPMC7544360 | biostudies-literature | 2020 Sep

REPOSITORIES: biostudies-literature