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A non-autonomous scalar one-dimensional dissipative parabolic problem: the description of the dynamics


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Title:
A non-autonomous scalar one-dimensional dissipative parabolic problem: the description of the dynamics
Authors:
de Cássia D S Broche, Rita
Carvalho, Alexandre
Valero, José  
Editor:
IOP Publishing
Department:
Departamentos de la UMH::Estadística, Matemáticas e Informática
Issue Date:
2019-10-30
URI:
https://hdl.handle.net/11000/32595
Abstract:
The purpose of this paper is to give a characterization of the structure of nonautonomous attractors of the problem ut = uxx + u 􀀀 (t)u3 when the parameter > 0 varies. Also, we answer a question proposed in [11], concerning the complete description of the structure of the pullback attractor of the problem when 1 < < 4 and, more generally, for ̸= N2, 2 N 2 N. We construct global bounded solutions , “non-autonomous equilibria”, connections between the trivial solution and these “non-autonomous equilibria” and characterize the -limit and !-limit set of global bounded solutions. As a consequence, we show that the global attractor of the associated skew-product flow has a gradient structure. The structure of the related pullback an uniform attractors are derived from that.
Knowledge area:
CDU: Ciencias puras y naturales: Matemáticas
Type of document:
application/pdf
Access rights:
info:eu-repo/semantics/openAccess
DOI:
https://doi.org/10.1088/1361-6544/ab3f55
Appears in Collections:
Artículos Estadística, Matemáticas e Informática



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