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da Silva, Severino Horácio; Ferreira, Jocirei Dias; Bezerra, Flank David Morais

Normal hyperbolicity and continuity of global attractors for a nonlocal evolution equation. (English) Zbl 1293.35353

Int. J. Differ. Equ. 2014, Article ID 625271, 13 p. (2014).
Summary: We show the normal hyperbolicity property for the equilibria of the evolution equation \(\partial m(r,t)\partial t= -m(r,t)+ g(\beta J\ast m(r,t)+\beta h)\), \(h,\beta \geq 0\), and using the normal hyperbolicity property we prove the continuity (upper semicontinuity and lower semicontinuity) of the global attractors of the flow generated by this equation, with respect to the functional parameter \(J\).

MSC:

35R09 Integro-partial differential equations
35B41 Attractors

Keywords:

nonlocal evolution equations; normal hyperbolicity; global attractors
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\textit{S. H. da Silva} et al., Int. J. Differ. Equ. 2014, Article ID 625271, 13 p. (2014; Zbl 1293.35353)
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References:

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