Global classical solutions for a class of reaction-diffusion system with density-suppressed motility

This paper is concerned with a class of reaction-diffusion system with density-suppressed motility  ut = increment (gamma(v)u) + alpha uF(w), x e ohm, t 2), where alpha 0 on (0, +oo) and lim gamma(v) = 0. v ->+oo The intake rate function F satisfies F e C1([0, +oo)), F(0) = 0 and F 0 on (0, +oo). We show that the above system admits a unique global classical solution for all non-negative initial data u0 e W1,oo(ohm), v0 e W1,oo(ohm), w0 e W1,oo(ohm). Moreover, if there exist k > 0 and v > 0 such that inf v>v vk gamma(v) > 0, then the global solution is bounded uniformly in time.

Automated summary

This paper investigates a class of reaction-diffusion system with density-suppressed motility. The paper proves the existence of a unique global classical solution for the system and shows that the solution is uniformly bounded in time under certain conditions.