- Tytuł:
- Wellposedness and exponential decay rates for the Moore-Gibson-Thompson equation arising in high intensity ultrasound
- Autorzy:
-
Kaltenbacher, B.
Lasiecka, I.
Marchand, R. - Powiązania:
- https://bibliotekanauki.pl/articles/206112.pdf
- Data publikacji:
- 2011
- Wydawca:
- Polska Akademia Nauk. Instytut Badań Systemowych PAN
- Tematy:
-
high intensity ultrasound
strongly continuous semigroup
exponential stability - Opis:
- 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.
- Źródło:
-
Control and Cybernetics; 2011, 40, 4; 971-988
0324-8569 - Pojawia się w:
- Control and Cybernetics
- Dostawca treści:
- Biblioteka Nauki
Artykuł