Abstract
For a singularly perturbed equation of inhomogeneous Allen-Cahn type with positive potential function in high dimensional general domain, we prove the existence of solutions, at least for some sequence of the positive parameter, which have clustered phase transition layers with mass centered close to a smooth closed stationary and non-degenerate hypersurface. Moreover, the interaction between neighboring layers is governed by a type of Jacobi-Toda system.
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.