Katharina Post
A Non-linear Parabolic System Modeling Chemotaxis with Sensitivity Functions
Preprint series: Institut fr Mathematik, Humboldt-Universitt zu Berlin (ISSN 0863-0976)

MSC:

35K57 Reaction-diffusion equations

35B40 Asymptotic behavior of solutions

Abstract: We study a model for chemotaxis on a general Lipschitz domain where the chemotactic response is specified by sensitivity functions. After finding a Lyapunov function for the system, we demonstrate existence of global solutions for different classes of sensitivity functions and show convergence to possibly non-trivial steady states.
Keywords: reaction-diffusion equations, a-priori-estimates, Lyapunov function, asymptotic behaviour, chemotaxis