Microlocal energy density for hyperbolic systems (CROSBI ID 485485)
Prilog sa skupa u zborniku | sažetak izlaganja sa skupa | međunarodna recenzija
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