Geodesic
The modeling of some optical systems on the base of parabolic differential-difference equation
Matematičeskoe modelirovanie, Tome 24 (2012) no. 12, pp. 38-42.

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The model of an optical system with field's transformation in two-dimensional feedback is considered. Such a system is described by the second boundary value problem for quasilinear parabolic equation with transformations of the space variables. The case of irreversible transformations of space variables (shifts) in the terms with second derivatives is considered.
Keywords: functional-differential equations, smoothness of solution. 
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A. M. Selitskii. The modeling of some optical systems on the base of parabolic differential-difference equation. Matematičeskoe modelirovanie, Tome 24 (2012) no. 12, pp. 38-42. http://geodesic.mathdoc.fr/item/MM_2012_24_12_a6/

[1] Vorontsov M. A., Dumarevskii Yu. D., Pruidze D. V., Shmalgauzen V. I., “Avtovolnovye protsessy v sistemakh s opticheskoi obratnoi svyazyu”, Izv. AN SSSR, Fizika, 52:2 (1988), 374–376

[2] Vorontsov M. A., Iroshnikov N. G., Abernathy R. L., “Diffractive patterns in nonlinear optical two-dimensional feedback system with field rotation”, Chaos Solitons Fractals, 4:8–9 (1994), 1701–1716 | DOI | Zbl

[3] Razgulin A. V., “Ob avtokolebaniyakh v nelineinoi parabolicheskoi zadache s preobrazovannym argumentom”, Zh. vychisl. matem. i matem. fiz., 33:1 (1993), 69–80 | MR | Zbl

[4] Razgulin A. V., “Rotational multi-petal waves in optical system with 2-D feedback”, Chaos in Optics, Proc. SPIE, 2039, ed. R. Roy, 1993, 342–352

[5] Skubachevskii A. L., “O nekotorykh svoistvakh ellipticheskikh i parabolicheskikh funktsionalno-differentsialnykh uravnenii”, Uspekhi mat. nauk, 51:1(307) (1996), 169–170 | MR

[6] Varfolomeev E. M., “O nekotorykh svoistvakh ellipticheskikh i parabolicheskikh funktsionalno-differentsialnykh operatorov, voznikayuschikh v nelineinoi optike”, Sovremennaya matematika. Fundamentalnye napravleniya, 21 (2008), 5–36 | MR | Zbl

[7] Razgulin A. V., “Proektsionno-raznostnaya skhema dlya parabolicheskogo funktsionalno-differentsialnogo uravneniya s dvumernym preobrazovaniem argumentov”, Zh. vychisl. matem. i matem. fiz., 245:10 (2005), 1848–1859 | MR

[8] Shamin R. V., Druzhinin V. A., “O modelirovanii nelineinykh evolyutsionnykh funktsionalno-differentsialnykh uravnenii”, Nelineinye granichnye zadachi, 2006, no. 16, 226–232 | MR | Zbl

[9] Selitskii A. M., Skubachevskii A. L., “Vtoraya kraevaya zadacha dlya parabolicheskogo differentsialno-raznostnogo uravneniya”, Trudy seminara im. I. G. Petrovskogo, 26, 2007, 323–346 | MR

[10] Shamin R. V., Skubachevskii A. L., “The mixed boundary value problem for parabolic differential-difference equation”, Functional differential equations, 8:3–4 (2001), 407–424 | MR | Zbl

[11] Lions J. L., “Espaces d'interpolation et domaines de puissances fractionnaires d'operateurs”, J. Math. Soc. Japan, 14:2 (1962), 233–241 | DOI | MR | Zbl

[12] Tsvetkov E. L., “Razreshimost i spektr tretei kraevoi zadachi dlya ellipticheskogo differentsialno-raznostnogo uravneniya”, Matem. zametki, 51:6 (1992), 107–114 | MR | Zbl

[13] Skubachevskii A. L., Tsvetkov E. L., “Vtoraya kraevaya zadacha dlya ellipticheskikh differentsialno-raznostnykh uravnenii”, Diff. uravn., 25:10 (1989), 1766–1776 | MR