Asymptotic behaviors and existence of traveling wave solutions to the Keller-Segel model with logarithmic sensitivity
This paper is concerned with the existence of traveling wave solutions for the Keller-Segel model with logarithmic sensitivity. By the Hopf-Cole transformation and traveling wave transformation, the degenerate Keller-Segel system is transformed into a singularly perturbed system. By constructing an invariant region to prove the existence of the traveling wave solutions for the degenerate system, the author obtains the traveling wave solutions for the Keller-Segel system with small parameters by means of geometric singular perturbation theory and Fredholm theory. Finally, the asymptotic behaviour of the travelling wave solutions is discussed.
scientific article; zbMATH DE number 7622282
scientific article