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Abstract: An analysis of traveling wave solutions of partial differential equationPDE systems with cross-diffusion is presented. The systems under study fallin a general class of the classical Keller-Segel models to describe chemotaxis.The analysis is conducted using the theory of the phase plane analysis of thecorresponding wave systems without a priory restrictions on the boundaryconditions of the initial PDE. Special attention is paid to families oftraveling wave solutions. Conditions for existence of front-impulse,impulse-front, and front-front traveling wave solutions are formulated. Inparticular, the simplest mathematical model is presented that has animpulse-impulse solution; we also show that a non-isolated singular point inthe ordinary differential equation ODE wave system implies existence offree-boundary fronts. The results can be used for construction and analysis ofdifferent mathematical models describing systems with chemotaxis.



Author: Faina Berezovskaya, Artem Novozhilov, Georgy Karev

Source: https://arxiv.org/







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