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On a Class of Linear Cooperative Systems with Spatio-temporal Degenerate Potentials
Title: On a Class of Linear Cooperative Systems with Spatio-temporal Degenerate Potentials
Authors: Álvarez Caudevilla, PabloBelinchón Martín, FernandoAutor AEMETBrandle Cerquiera, Cristina
Keywords: Eigenvalue problems; Asymptotic analysis; Degenerate potentials; Spatio-temporal coefficients
Issue Date: 2021
Publisher: Springer
Citation: Mediterranean Journal of Mathematics. 2021, 18(249), p. 1-27
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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.
ISSN: 1660-5446
Appears in Collections:Artículos científicos 2000-2004

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