Global boundedness and large time behavior of solutions to a chemotaxis-consumption system with signal-dependent motility

This paper deals with the following chemotaxis-consumption system with signal-dependent motility {u(t) = Delta(gamma(v)u), x is an element of Omega, t > 0, v(t) = Delta v - uv, x is an element of Omega, t > 0, under no-flux boundary conditions in a smoothly bounded domain Omega subset of R-n. gamma(s) is the motility function. For the case of positive motility function, it is shown that the corresponding initial boundary value problem possesses a unique global classical solution which is uniformly bounded. Moreover, it is asserted that the solution to the system exponentially converges to constant equilibria in the large time. Finally, if the motility function is zero at some point, we obtain the existence of the weak solution.

Automated summary

This paper discusses the behavior of a chemotaxis-consumption system with signal-dependent motility in a smoothly bounded domain Omega. The study shows that for the case of positive motility function, the system has a unique global classical solution which is uniformly bounded, and the solution exponentially converges to constant equilibria in the large time. Additionally, the existence of weak solution is obtained when the motility function is zero at some point.