We study a quasilinear parabolic-parabolic chemotaxis system with nonlinear logistic source, under homogeneous Neumann boundary conditions in a smooth bounded domain. By establishing proper a priori estimates we prove that, with both the diffusion function and the chemotaxis sensitivity function being positive, the corresponding initial boundary value problem admits a unique global classical solution which is uniformly bounded. The result of this paper is a generalization of that of Cao (2014)., Ji Liu, Jia-Shan Zheng., and Obsahuje seznam literatury
This paper deals with parabolic-elliptic chemotaxis systems with the sensitivity function χ(v) and the growth term f(u) under homogeneous Neumann boundary conditions in a smooth bounded domain. Here it is assumed that 0 < χ(v) ≤ χ0/vk (k ≥ 1, χ0 > 0) and λ1 − µ1u ≤ f(u) ≤ λ2 − µ2u (λ1, λ2, µ1, µ2 > 0). It is shown that if χ0 is sufficiently small, then the system has a unique global-in-time classical solution that is uniformly bounded. This boundedness result is a generalization of a recent result by K. Fujie, M. Winkler, T. Yokota.
Resveratrol, which is a polyphenol present in red wines and vegetables included in human diets, exerts many biological effects. The aim of the present study was to investigate its effect on some activities of polymorphonuclear leukocytes, particularly the generation of superoxide anion (O2-) in whole blood, hypochlorous acid (HOCl) and nitric oxide (NO) production by isolated cells, and chemotaxis. Resveratrol showed significant dose-dependent inhibitory effect on all these activities. In particular, it inhibited O2- generation in stimulated but not in resting neutrophils, decreased HOCl much more than O2- production indicating an effect on myeloperoxidase secretion since HOCl production is directly and proportionally dependent on O2- generation and reduced cell motility. The small dose of resveratrol (4.38 nM) used is attainable with a diet including red wine and vegetables confirming its protective role against some pathological processes such as inflammation, coronary heart disease, and cancer., A. Cavallaro, T. Ainis, C. Bottari, V. Fimiani., and Obsahuje bibliografii
We study a class of parabolic-ODE systems modeling tumor growth, its mathematical modeling and the global in time existence of the solution obtained by the method of Lyapunov functions.