GLOBAL BOUNDEDNESS OF CLASSICAL SOLUTIONS TO A LOGISTIC CHEMOTAXIS SYSTEM WITH SINGULAR SENSITIVITY

We consider a chemotaxis system with singular sensitivity and logistic-type source: u(t) = Delta u - chi del . (u/v del v) + ru - mu u(k), v(t) = epsilon Delta v - v + u in a smooth bounded domain Omega subset of R-n with chi, r, mu, epsilon > 0, k > 1 and n >= 2. It is proved that the system possesses a globally bounded classical solution when epsilon+chi < 1. This shows that the diffusive coefficient epsilon of the chemical substance v properly small benefits the global boundedness of solutions, without the restriction on the dampening exponent k > 1 in logistic source.