Abstract
For a system of semilinear elliptic partial differential equations with a small parameter, denned on a bounded multi-dimensional smooth domain, we show the existence of solutions with internal layers. The high-dimensionality of the domain gives rise to quite interesting an outlook in the analysis, dramatically different from that in one-dimensional settings. Our analysis indicates, in a certain situation, an occurrence of an infinite series of bifurcation phenomena accumulating as the small parameter goes to zero. We also present a related free boundary problem with a possible approach to its resolution.
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 callMore From: Proceedings of the Royal Society of Edinburgh: Section A Mathematics
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.
