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Microlocal energy density for hyperbolic systems (CROSBI ID 485485)

Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija

Lazar, Martin ; Antonić, Nenad Microlocal energy density for hyperbolic systems // Applied Mathematics and Scientific computing / Drmač, Z.; Hari V.; Sopta L. et al. (ur.). Zagreb: Matematički odsjek Prirodoslovno-matematičkog fakulteta Sveučilišta u Zagrebu, 2001. str. 14-14-x

Podaci o odgovornosti

Lazar, Martin ; Antonić, Nenad

engleski

Microlocal energy density for hyperbolic systems

Starting from the method for computing microlocal energy density, which was developed independently by G\'erard, and Francfort and Murat, we want to compute that very density for the hyperbolic system $$ A^0 \partial_0 v + \sum_1^d A^k \partial_k v + Bv = G. $$ The energy connected to the hyperbolic system is given by the relation $$ E:={1 \over 2} \langle A^0 v, v\rangle. $$ We want to express the energy limit of the sequence of initial problems with the energy of initial conditions. The basic calculus tool 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 have determined the equation satisfied by the corresponding H-measure. In the case of the constant coefficients it reduces to a hyperbolic system similar to the initial one. Rewriting the wave equation as a hyperbolic system, we calculated the associated H-measure for the oscillating sequence of the initial conditions. The result is analogous to the one obtained by the direct calculus of H-measure from the D'Alembert's formula for the solution of the wave equation.

H-measure; hyperbolic system

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Podaci o prilogu

14-14-x.

2001.

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objavljeno

Podaci o matičnoj publikaciji

Applied Mathematics and Scientific computing

Drmač, Z.; Hari V.; Sopta L.; Tutek Z.; Veselić K.

Zagreb: Matematički odsjek Prirodoslovno-matematičkog fakulteta Sveučilišta u Zagrebu

Podaci o skupu

Applied Mathematics and Scientific computing

predavanje

04.06.2001-08.06.2001

Dubrovnik, Hrvatska

Povezanost rada

Matematika