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On a Class of Linear Cooperative Systems with Spatio-temporal Degenerate Potentials
Título : On a Class of Linear Cooperative Systems with Spatio-temporal Degenerate Potentials
Autor : Álvarez Caudevilla, PabloBelinchón Martín, FernandoAutor AEMETBrandle Cerquiera, Cristina
Palabras clave : Eigenvalue problems; Asymptotic analysis; Degenerate potentials; Spatio-temporal coefficients
Fecha de publicación : 2021
Editor: Springer
Citación : Mediterranean Journal of Mathematics. 2021, 18(249), p. 1-27
Versión del editor: https://doi.org/10.1007/s00009-021-01913-3
Resumen : 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.
URI : http://hdl.handle.net/20.500.11765/15358
ISSN : 1660-5446
1660-5454
Colecciones: Artículos científicos 2000-2004


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