Global boundedness of solutions to a chemotaxis consumption model with signal dependent motility and logistic source

This paper deals with the following chemotaxis system: {u(t )= del<middle dot>gamma(v)del u-u xi(v)del v)+mu u(1-u), x is an element of Omega,t > 0, v(t )= Delta v-uv, x is an element of Omega,t > 0 under homogeneous Neumann boundary conditions in a bounded domain Omega subset of & Ropf;n,n >= 2, with smooth boundary. Here, the functions gamma(v) and xi(v) are as: gamma(v) = (1+v)(-k )and xi(v) = -(1-alpha)gamma '(v) where k > 0 and alpha is an element of(0,1). For the above system, we prove that the corresponding initial boundary value problem admits a unique global classical solution which is uniformly-in-time bounded. This result is obtained under some conditions on initial value v(0) and mu and without any restriction on k and alpha. The obtained result extends the recent results obtained for this problem.