BOUNDEDNESS IN A CHEMOTAXIS-MAY-NOWAK MODEL FOR VIRUS DYNAMICS WITH MILDLY SATURATED CHEMOTACTIC SENSITIVITY AND CONVERSION

This work studies a class of chemotaxis systems given by ut = increment u - V middot (uf (u)Vv) - u - g(u)w + Kappa,vt = increment v - v + g(u)w,wt = increment w - w + v,under homogeneous Neumann boundary conditions in smooth bounded n dimensional domains, where Kappa > 0, f E C2([0, oo)) satisfies |f (s)| < Kf(1 + s)-alpha for all s > 0 with some Kf > 0 and alpha E R, and g E C1([0, oo)) is a nonnegative function satisfying g(0) = 0 and g(s) < Kg(1 + s beta) for all s > 1 with Kg > 0 and beta E R. Under the assumption that beta < n2 (n > 2), it is shown that there exists alpha 0 = alpha 0(beta) > 0 such that if alpha > -alpha 0, then the system has a global classical solution which is uniformly bounded. The case when n = 1 is also discussed. These improve the known results.