Naslov
Microlocal energy density for hyperbolic systems

Autori
Antonić, Nenad ; Lazar, Martin

Vrsta, podvrsta i kategorija rada
Radovi u zbornicima skupova, cjeloviti rad (in extenso), znanstveni

Izvornik
Proceedings of the Conference on Applied Mathematics and Scientific Computing / Drmač, Zlatko ; Hari, Vjeran ; Sopta, Luka ; Tutek, Zvonimir ; Veselić, Krešimir - New York (NY) : Kluwer Academic Publishers ; Plenum Publishers, 2003, 179-190

ISBN
0-306-47426-3

Skup
Conference on Applied Mathematics and Scientific Computing

Mjesto i datum
Dubrovnik, Hrvatska, 04.06.2001. - 09.06.2001

Vrsta sudjelovanja
Predavanje

Vrsta recenzije
Međunarodna recenzija

Ključne riječi
H-measure; hyperbolic system

Sažetak
Starting from the method for computing microlocal energy density, which was developed independently by Francfort and Murat, and G\'erard for the linear wave equation, we compute that very density for the hyperbolic system $$ \mA^0 \partial_0 \vv + \sum_1^d \mA^k \partial_k \vv + \mB\vv = \vf. $$ We express the energy limit for the sequence of initial problems in terms of the energy of initial conditions. The basic tool we use are H-measures (also known as microlocal defect measures). We associate an H-measure to the sequence of gradients of solutions to our system and it represents the desired microlocal energy density. We determine the system of equations satisfied by the corresponding H-measure. In the case of constant coefficients it reduces to a hyperbolic system similar to the initial one. Finally, we give a few examples related to the wave equation.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

POVEZANOST RADA