Naslov
Microlocal energy density for hyperbolic systems

Autori
Lazar, Martin ; Antonić, Nenad

Vrsta, podvrsta i kategorija rada
Sažeci sa skupova, sažetak, znanstveni

Izvornik
Applied Mathematics and Scientific computing / Drmač, Z.; Hari V.; Sopta L.; Tutek Z.; Veselić K. - Zagreb : Matematički odsjek Prirodoslovno-matematičkog fakulteta Sveučilišta u Zagrebu, 2001, 14-14

Skup
Applied Mathematics and Scientific computing

Mjesto i datum
Dubrovnik, Hrvatska, 04.06.2001. - 08.06.2001

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 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.

Izvorni jezik
Engleski

Znanstvena područja
Matematika

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