Abstract
Abstract We investigate traveling wave solutions for a nonlinear system of two coupled reaction-diffusion equations characterized by double degenerate diffusivity: n t = − f ( n , b ) , b t = [ g ( n ) h ( b ) b x ] x + f ( n , b ) . These systems mainly appear in modeling spatio-temporal patterns during bacterial growth. Central to our study is the diffusion term g ( n ) h ( b ) , which degenerates at n = 0 and b = 0; and the reaction term f ( n , b ) , which is positive, except for n = 0 or b = 0. Specifically, the existence of traveling wave solutions composed by a couple of strictly monotone functions for every wave speed in a closed half-line is proved, and some threshold speed estimates are given. Moreover, the regularity of the traveling wave solutions is discussed in connection with the wave speed.
Published Version
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