Global Existence of Classical Solutions to an Aggregation Model with Logistic Source

In this article, a class of systems of cross-diffusion chemotaxis is studied. Using the entropy dissipation method and assuming that chemotactic sensitivity mainly separates cell density and chemical signal, it is established the existence of global solutions with cross-diffusion effects. The global existence and uniqueness of the classical solutions of this system is proved by the contraction mapping principle using a priori $$L^{p}$$ estimates and Schauder type estimates for parabolic equations.

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