Abstract
We study the large time behaviour of the reaction-diffusion equation ∂tu=Δu+f(u) in spatial dimension N, when the non-linear term is bistable and the initial datum is compactly supported. We prove the existence of a Lipschitz function s∞ of the unit sphere, such that u(t,x) converges uniformly in RN, as t goes to infinity, to Uc⁎(|x|−c⁎t+N−1c⁎lnt+s∞(x|x|)), where Uc⁎ is the unique 1D travelling profile. This extends earlier results that identified the locations of the level sets of the solutions with ot→+∞(t) precision, or identified precisely the level sets locations for almost radial initial data.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
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.