On the well-posedness of the Cauchy problem for the system of equations of chemotaxis
This paper is devoted to the initial boundary value problem for the system of equations of chemotaxis. The existence and uniqueness of a classical solution to the problem are proved for the original problem with nonzero diffusivities. For the reduced problem with zero diffusivities, the existence of a functional solution is proved. The existence of a Sobolev solution to the former problem is proved by taking the limit value of one of the diffusivities.
scientific article; zbMATH DE number 1940643