Abstract
We show that long time solution dynamic for general reaction-advection-diffusion equations with KPP reactions is virtually linear in the following sense. Its leading order depends on the non-linear reaction only through its linearization at u=0, and it can also be recovered for general initial data by instead solving the PDE for restrictions of the initial condition to unit cubes on Rd (the latter means that non-linear interaction of these restricted solutions has only lower order effects on the overall solution dynamic). The result holds under a uniform bound on the advection coefficient, which we show to be sharp. We also extend it to models with non-local diffusion and KPP reactions.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: 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.
