Abstract
Previous studies of chemotaxis models with consumption of the chemoattractant (with or without fluid) have not been successful in explaining pattern formation even in the simplest form of concentration near the boundary, which had been experimentally observed. Following the suggestions that the main reason for that is the usage of inappropriate boundary conditions, in this paper we study the solutions to the stationary chemotaxis system [Formula: see text] in bounded domains [Formula: see text], [Formula: see text], under the no-flux boundary conditions for [Formula: see text] and the physically meaningful condition [Formula: see text] on [Formula: see text], with the given parameter [Formula: see text] and [Formula: see text], [Formula: see text], satisfying [Formula: see text], [Formula: see text] on [Formula: see text]. We prove the existence and uniqueness of solutions for any given mass [Formula: see text]. These solutions are nonconstant.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
More From: Mathematical Models and Methods in Applied Sciences
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.