Global existence of a quasilinear chemotaxis model with signal-dependent motility and indirect signal production mechanism

In this paper, we study the following quasilinear chemotaxis model with signal-dependent motility: n(t) = Delta(gamma(c)n(m)); c(t) = d(c)Delta c - c + v; v(t) = d(v)Delta v - v + n, x is an element of Omega, t > 0, partial derivative(n(m)gamma(c))/partial derivative nu = partial derivative c/partial derivative nu = partial derivative v/partial derivative nu = 0, x is an element of partial derivative Omega, t > 0, n(x, 0) = n(0)(x), c(x, 0) = c(0)(x), v(x, 0) = v(0)(x), x is an element of Omega, t > 0, where gamma(c) = c(-r). We show that the above system admits at least one global weak solution. Published under an exclusive license by AIP Publishing.

Automated summary

This paper studies a quasilinear chemotaxis model with signal-dependent motility and proves the existence of at least one global weak solution for the system.