Microlocal energy density for hyperbolic systems (CROSBI ID 489618)
Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija
Podaci o odgovornosti
Antonić, Nenad ; Lazar, Martin
engleski
Microlocal energy density for hyperbolic systems
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.
H-measure; hyperbolic system
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Podaci o prilogu
179-190.
2003.
objavljeno
Podaci o matičnoj publikaciji
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
0-306-47426-3
Podaci o skupu
Conference on Applied Mathematics and Scientific Computing
predavanje
23.06.2003-27.06.2003
Brijuni, Hrvatska