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On exponential stability for von Kármán equations in the presence of thermal effects
Author(s) -
Bisognin E.,
Bisognin V.,
Perla Menzala G.,
Zuazua E.
Publication year - 1998
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/(sici)1099-1476(19980325)21:5<393::aid-mma958>3.0.co;2-j
Subject(s) - compact space , mathematics , bounded function , exponential stability , energy (signal processing) , nonlinear system , exponential growth , mathematical analysis , exponential function , space (punctuation) , mathematical physics , exponential decay , pure mathematics , physics , quantum mechanics , linguistics , statistics , philosophy
We consider a dynamical von Kármán system in the presence of thermal effects. Our model includes the possibility of a rotational inertia term in the system. We show that the total energy of the solution of such system decays exponentially as t →+∞. The decay rates we obtain are uniform on bounded sets of the energy space. The main ingredients of our method of proof are suitable properties of a decoupled system, the energy method and the compactness of the nonlinear map associated to the von Kármán system. © 1998 B. G. Teubner Stuttgart–John Wiley & Sons Ltd.