Abstract
This paper analyses a class of parabolic linear cooperative systems in a cylindrical domain with degenerate spatio-temporal potentials. In other words, potentials vanish in some non-empty connected subdomains which are disjoint and increase in size temporally. Then, the vanishing subdomains for the potentials are not cylindrical. Following a similar idea to the semiclassical analysis behaviour, but done here for parabolic problems, under these geometrical assumptions, the asymptotic behaviour of the system is ascertained when a parameter, in front of these potentials, goes to infinity. In particular, the strong convergence of the solutions of the system is obtained using energy methods and the theory associated with the Gamma -convergence. Also, the exponential decay of the solutions to zero in the exterior of the subdomains where the potentials vanish is achieved.
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.