Geodesic
A Mixed Problem for the Dirac--Schwinger Extension of the Maxwell System
Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 184-199.

Voir la notice de l'article provenant de la source Math-Net.Ru

The paper is devoted to the topical, but insufficiently studied problem of finding conditions for the solvability of a $L_2$-well-posed initial boundary-value problem for the linear system of four hyperbolic-type equations (Maxwell equations for the vector-potential) with dissipation, a zero initial condition, and an inhomogeneous boundary condition.
Keywords: Maxwell system of equations, Dirac–Schwinger extension of the Maxwell system, hyperbolic-type equation, nonequilibrium process, pseudodifferential operator, initial boundary-value problem
Mots-clés : Fourier transform. 
@article{MZM_2012_91_2_a2,
     author = {I. V. Zagrebaev},
     title = {A {Mixed} {Problem} for the {Dirac--Schwinger} {Extension} of the {Maxwell} {System}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {184--199},
     publisher = {mathdoc},
     volume = {91},
     number = {2},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a2/}
}
TY  - JOUR
AU  - I. V. Zagrebaev
TI  - A Mixed Problem for the Dirac--Schwinger Extension of the Maxwell System
JO  - Matematičeskie zametki
PY  - 2012
SP  - 184
EP  - 199
VL  - 91
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a2/
LA  - ru
ID  - MZM_2012_91_2_a2
ER  - 
%0 Journal Article
%A I. V. Zagrebaev
%T A Mixed Problem for the Dirac--Schwinger Extension of the Maxwell System
%J Matematičeskie zametki
%D 2012
%P 184-199
%V 91
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a2/
%G ru
%F MZM_2012_91_2_a2
I. V. Zagrebaev. A Mixed Problem for the Dirac--Schwinger Extension of the Maxwell System. Matematičeskie zametki, Tome 91 (2012) no. 2, pp. 184-199. http://geodesic.mathdoc.fr/item/MZM_2012_91_2_a2/

[1] I. Müller, T. Ruggeri, Extended Thermodynamics, Springer Tracts Nat. Philos., 37, Springer-Verlag, New York, 1993 | MR

[2] H. Struchtrup, W. Weiss, “Temperature jump and velocity slip in the moment method”, Contin. Mech. Thermodyn., 12:1 (2000), 1–18 | DOI | MR | Zbl

[3] R. Peierls, “Zur kinetischen Theorie der Wärmeleitung in Kristallen”, Ann. Phys., 395:8 (1929), 1055–1101 | DOI | Zbl

[4] H.-O. Kreiss, “Initial boundary value problems for hyperbolic systems”, Comm. Pure Appl. Math., 23 (1970), 277–298 | MR | Zbl

[5] E. V. Radkevich, “Irreducible Chapman–Enskog projections and Navier–Stokes approximations”, Instability in Models Connected with Fluid Flows. II, Int. Math. Ser. (N. Y.), 7, Springer-Verlag, New York, 2008, 85–153 | MR

[6] E. V. Radkevich, “Kineticheskie uravneniya i problemy proektsii Chepmena–Enskoga”, Differentsialnye uravneniya i dinamicheskie sistemy, Sbornik statei, Tr. MIAN, 250, Nauka, M., 2005, 219–225 | MR | Zbl

[7] E. V. Radkevich, Matematicheskie voprosy neravnovesnykh protsessov, Belaya seriya, 4, Izd-vo “Tamara Rozhkovskaya”, Novosibirsk, 2007

[8] S. Chapman, T. Cowling, Mathematical Theory on Non-Uniform Gases. An Account of the Kinetic Theory of Viscosity, Thermal Conduction and Diffusion in Gases, Cambridge Univ. Press, Cambridge, 1970 | MR

[9] V. V. Palin, “O razreshimosti kvadratnykh matrichnykh uravnenii”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2008, no. 6, 36–41 | MR