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Control and Cybernetics

Tytuł artykułu

Wellposedness and exponential decay rates for the Moore-Gibson-Thompson equation arising in high intensity ultrasound

Autorzy Kaltenbacher, B.  Lasiecka, I.  Marchand, R. 
Treść / Zawartość
Warianty tytułu
Języki publikacji EN
EN We consider the Moore-Gibson-Thompson equation which arises, e.g., as a linearization of a model for wave propagation in viscous thermally relaxing fluids. This third order in time equation displays, even in the linear version, a variety of dynamical behaviors for their solutions that depend on the physical parameters in the equation. These range from non-existence and instability to exponential stability (in time). It will be shown that by neglecting diffusivity of the sound coefficient there arises a lack of existence of a semigroup associated with the linear dynamics. More specifically, the corresponding linear dynamics consists of three diffusions: two backward and one forward. When diffusivity of the sound is positive, the linear dynamics is described by a strongly continuous semigroup which is exponentially stable when the ratio of sound speed×relaxation parameter/ sound diffusivity is sufficiently small, and unstable in the complementary regime. The theoretical estimates proved in the paper are confirmed by numerical validation.
Słowa kluczowe
EN high intensity ultrasound   strongly continuous semigroup   exponential stability  
Wydawca Systems Research Institute, Polish Academy of Sciences
Czasopismo Control and Cybernetics
Rocznik 2011
Tom Vol. 40, no 4
Strony 971--988
Opis fizyczny Bibliogr. 20 poz., wykr.
autor Kaltenbacher, B.
autor Lasiecka, I.
autor Marchand, R.
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