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Nonclassical diffusion with memory
Author(s) -
Conti Monica,
Marchini Elsa M.,
Pata Vittorino
Publication year - 2014
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.3120
Subject(s) - mathematics , semigroup , bounded function , domain (mathematical analysis) , kernel (algebra) , attractor , diffusion , pure mathematics , mathematical analysis , physics , thermodynamics
We consider the nonclassical diffusion equation with hereditary memoryu t − Δ u t − Δu − ∫ 0 ∞ κ ( s ) Δu ( t − s ) d s + φ ( u ) = f on a bounded three‐dimensional domain. Setting the problem in the past history framework, and with very general assumptions on the memory kernel κ , we prove that the related solution semigroup possesses a global attractor of optimal regularity. Copyright © 2014 John Wiley & Sons, Ltd.
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