The third boundary-value problem for parabolic differential-difference equations

A. M. Selitskii

Contemporary Mathematics. Fundamental Directions, Proceedings of the Seminar on Differential and Functional Differential Equations supervised by A. L. Skubachevskii (Peoples' Friendship University of Russia), Tome 21 (2007), pp. 114-132.

Bibliographie

[1] Vlasov V. V., “O razreshimosti i svoistvakh reshenii funktsionalno-differentsialnykh uravnenii v gilbertovom prostranstve”, Mat. sbornik, 186:8 (1995), 67–92 | MR | Zbl

[2] Vlasov V. V., “O razreshimosti i otsenkakh reshenii funktsionalno-differentsialnykh uravnenii v prostranstvakh Soboleva”, Tr. MIAN, 227, 1999, 109–121 | Zbl

[3] Kamenskii G. A., Skubachevskii A. L., Lineinye kraevye zadachi dlya differentsialno-raznostnykh uravnenii, MAI, M., 1992

[4] Kato T., Teoriya vozmuschenii lineinykh operatorov, Mir, M., 1972

[5] Lions Zh.-L., Optimalnoe upravlenie sistemami, opisyvaemymi uravneniyami s chastnymi proizvodnymi, Mir, M., 1972

[6] Lions Zh.-L., Madzhenes E., Neodnorodnye granichnye zadachi i ikh prilozheniya, Mir, M., 1971

[7] Mikhailov V. P., Differentsialnye uravneniya v chastnykh proizvodnykh, Nauka, M., 1983

[8] Selitskii A. M., Skubachevskii A. L., “Vtoraya kraevaya zadacha dlya parabolicheskogo differentsialno-raznostnogo uravneniya”, Tr. sem. im. I. G. Petrovskogo, 26 (2007) (to appear) | MR

[9] Skubachevskii A. L., “O bifurkatsii Khopfa dlya kvazilineinogo parabolicheskogo funktsionalno-differentsialnogo uravneniya”, Diff. uravn., 34:10 (1998), 1394–1401 | MR | Zbl

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

[11] Skubachevskii A. L., Shamin R. V., “Pervaya smeshannaya zadacha dlya parabolicheskogo differentsialno-raznostnogo uravneniya”, Mat. zametki, 66:1 (1999), 145–153 | MR | Zbl

[12] Tribel Kh., Teoriya interpolyatsii, funktsionalnye prostranstva, differentsialnye operatory, Mir, M., 1980

[13] Shamin R. V., “O prostranstvakh nachalnykh dannykh dlya differentsialnykh uravnenii v gilbertovom prostranstve”, Mat. sbornik, 194:9 (2003), 141–156 | MR | Zbl

[14] Ashyralyev A., Sobolevskii P. E., Well-posedness of parabolic difference equations, Birkhäuser, Basel—Boston—Berlin, 1994 | MR

[15] Lions J. L., Magenes E., Non-homogeneous boundary value problems and applications, English translation, vol. 2, Springer-Verlag, New York–Heidelberg–Berlin, 1972

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

[17] Selitskii A. M., “The third boundary value problem for parabolic differential-difference equation in one-dimensional case”, Funct. Differ. Equ., 14:3–4 (2007) (to appear) | MR | Zbl

[18] Shamin R. V., “Nonlocal parabolic problems with the support of nonlocal terms inside a domain”, Funct. Differ. Equ., 10:1–2 (2003), 307–314 | MR | Zbl

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

[20] Skubachevskii A. L., Elliptic Functional Differential Equations and Applications, Birkhäuser, Basel–Boston–Berlin, 1997 | MR | Zbl

[21] Skubachevskii A. L., “Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics”, Nonlinear Anal., 32:2 (1998), 261–278 | DOI | MR | Zbl

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