The Existence of Positive Nonconstant Steady States in a Reaction: Diffusion Epidemic Model

Abstract

We investigate the disease’s dynamics of a reaction-diffusion epidemic model. We first give a priori estimates of upper and lower bounds for positive solutions to model and then give the conditions of the existence and nonexistence of the positive nonconstant steady states, which guarantees the existence of the stationary patterns.

Pattern Formation in a Bacterial Colony Model

“…In the present paper, it is to investigate the spatial pattern formation of system (1) which means the convergence of solutions to some stable spatially-in-homogeneous pattern as time tends to infinity. And in natural science, the pattern formation can reveal the evolution process of the species; it is, perhaps, the most challenging in modern ecology, biology, chemistry, and many other fields of science [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. Thus, our basic concern is to find, if any, a spatially inhomogeneous equilibrium and periodic solutions that are stable in a certain sense.…”