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Global and exponential attractors for 3‐D wave equations with displacement dependent damping
Author(s) -
Pata Vittorino,
Zelik Sergey
Publication year - 2006
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.726
Subject(s) - mathematics , dissipative system , attractor , semigroup , mathematical analysis , damped wave , exponential function , wave equation , displacement (psychology) , phase space , space (punctuation) , physics , quantum mechanics , psychology , psychotherapist , linguistics , philosophy
A weakly damped wave equation in the three‐dimensional (3‐D) space with a damping coefficient depending on the displacement is studied. This equation is shown to generate a dissipative semigroup in the energy phase space, which possesses finite‐dimensional global and exponential attractors in a slightly weaker topology. Copyright © 2006 John Wiley & Sons, Ltd.