Decay rates for partially dissipative hyperbolic systems
by
Enrique Zuazua
IMDEA-Mathematics & Universidad Autonoma de Madrid

We shall present recent results on the decay rates for linear partially dissipative hyperbolic systems on the whole space. It is by now well known that, under the Shizuta-Kawashima (SK) condition, solutions may be decomposed as a high frequency hyperbolic like component decaying exponentially as time goes to infinity plus a polynomially decaying component corresponding to the low frequencies. We first show that the condition SK is equivalent to the classical Kalman rank condition in finite dmensional control theory arising also in the analysis of hypoellipticity. In view of this, we show that, such a condition is not necessary for this kind of decomposition to hold. We also show that weaker rank conditions yield more general decompositions in which solutions may contain, in particular, components that decay more slowly. This lecture is based on joint work with Karine Beauchard, ENS, Cachan, France

Date received: July 2, 2007

Copyright © 2007 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cavj-74.