On a class of linear cooperative systems with spatio-temporal degenerate potentials Articles uri icon

publication date

  • December 2021

start page

  • 249

issue

  • 6

volume

  • 18

International Standard Serial Number (ISSN)

  • 1660-5446

Electronic International Standard Serial Number (EISSN)

  • 1660-5454

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 Γ-convergence. Also, the exponential decay of the solutions to zero in the exterior of the subdomains where the potentials vanish is achieved.

keywords

  • eigenvalue problems; asymptotic analysis; degenerate potentials; spatio-temporal coefficients