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Microlocal energy density for hyperbolic systems (CROSBI ID 489618)

Prilog sa skupa u zborniku | izvorni znanstveni rad | međunarodna recenzija

Antonić, Nenad ; Lazar, Martin Microlocal energy density for hyperbolic systems // Proceedings of the Conference on Applied Mathematics and Scientific Computing / Drmač, Zlatko ; Hari, Vjeran ; Sopta, Luka et al. (ur.). New York (NY): Kluwer Academic Publishers ; Plenum Publishers, 2003. str. 179-190

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

Povezanost rada

Matematika