Global existence of solutions to the chemotaxis system with logistic source under nonlinear Neumann boundary conditions

We consider classical solutions to the chemotaxis system with logistic source, au - mu u(2), under nonlinear Neumann boundary conditions partial derivative u/partial derivative v = |u|(p) with p > 1 in a smooth convex bounded domain Omega subset of R-n, where n >= 2. This paper aims to show that if p < 3/2, and mu > 0, n = 2, or mu is sufficiently large when n >= 3, then the parabolic-elliptic chemotaxis system admits a unique nonnegative global-in-time classical solution that is bounded in Omega x (0, infinity). The similar result is also true if p < 3/2, n = 2, and mu > 0 or p < 7/5, n = 3, and mu is sufficiently large for the parabolic-parabolic chemotaxis system.(c) 2023 Elsevier Inc. All rights reserved.

Automated summary

This paper investigates the classical solutions to the chemotaxis system with logistic source under nonlinear Neumann boundary conditions. It shows the existence and uniqueness of nonnegative global-in-time classical solutions under certain parameter conditions, and also extends the similar result to the parabolic-parabolic chemotaxis system.