Boundedness of solutions in a quasilinear chemo-repulsion system with nonlinear signal production

This paper deals with a quasilinear parabolic-elliptic chemo-repulsion system with nonlinear signal production {u(t) = del.(phi(u)del u) + chi del.(u(u + 1)(alpha-1) del v) + f(u), (x,t) is an element of Omega x (0, infinity), 0=Delta v - v +u(S), (x,t) is an element of Omega x (0, infinity), under homogeneous Neumann boundary conditions in a smoothly bounded domain Omega subset of R-n(n >= 1), where chi, beta > 0,alpha is an element of R, the nonlinear diffusion phi is an element of C-2([O, infinity)) satisfies phi(u) >= (u + 1)(m) with m is an element of R, and the function f is an element of C-1 ([0, infinity)) is a generalized growth term. When f 0, it is shown that the solution of the above system is global and uniformly bounded for all chi, beta > 0 and m, alpha is an element of R. When f not equivalent to 0 and assume that f(u) <= ku-bu(gamma+1) with k,b, gamma > 0, it is proved that the solution of the above system is also global and uniformly bounded for all chi, beta > 0 and m, alpha is an element of R.