Article PDF
Avoid common mistakes on your manuscript.
References
A. Ashyralyev and P. E. Sobolevskii, Well-Posedness of Parabolic Difference Equations, Birkhäuser, Basel-Boston-Berlin, (1994).
G. A. Kamenskii and A. L. Skubachevskii, Linear Boundary Value Problems for Differential-Difference Equations [in Russian], MAI, Moscow (1990).
T. Kato, Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).
J.-L. Lions, Optimal Control of Systems That Are Governed by Partial Differential Equations [Russian translation], Mir, Moscow (1972).
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary-Value Problems and Applications [Russian translation], Mir, Moscow (1971).
J.-L. Lions and E. Magenes, Non-Homogeneous Boundary Value Problems and Applications. Vol. 2, Springer-Verlag, New York-Heidelberg-Berlin (1972).
V. P. Mikhailov, Partial Differential Equations [in Russian], Nauka, Moscow (1983).
A. V. Razgulin, “Rotational multi-petal waves in optical systems with 2-D feedback,” Chaos in Optics. Proceedings SPIE, 2039, 342–352 (1993).
A. M. Selitskii, “The third boundary value problem for parabolic differential-difference equations in the one-dimensional case,” Funct. Differ. Equ., To appear.
A. M. Selitskii and A. L. Skubachevskii, “The second boundary-value problem for parabolic differential-difference equations,” Tr. Semin. im. I. G. Petrovskogo, To appear.
R. V. Shamin, “Spaces of initial data for differential equations in a Hilbert space,” Sb. Math., 194, No. 9–10, 1411–1426 (2003).
R. V. Shamin, “Nonlocal parabolic problems with the support of nonlocal terms inside a domain,” Funct. Differ. Equ., 10, No. 1–2, 307–314 (2003).
A. L. Skubachevskii, Elliptic Functional Differential Equations and Applications, Birkhäuser, Basel-Boston-Berlin, (1997).
A. L. Skubachevskii, “On the Hopf bifurcation for a quasilinear parabolic functional-differential equation,” Differ. Equ., 34, No. 10, 1395–1402 (1998).
A. L. Skubachevskii, “Bifurcation of periodic solutions for nonlinear parabolic functional differential equations arising in optoelectronics,” Nonlinear Anal, 32, No. 2, 261–278 (1998).
A. L. Skubachevskii and R. V. Shamin, “The first mixed problem for a parabolic differential-difference equation,” Math. Notes, 66, No. 1–2, 113–119 (1999).
A. L. Skubachevskii and R. V. Shamin, “The mixed boundary value problem for parabolic differential-difference equations,” Funct. Differ. Equ., 8, No. 3–4, 407–424 (2001).
A. L. Skubachevskii and E. L. Tsvetkov, “The second boundary value problem for elliptic differential-difference equations,” Differ. Equ., 25, No. 10, 1245–1254 (1989).
H. Triebel, Interpolation Theory, Function Spaces, Differential Operators, Ambrosius Barth, Heidelberg (1995).
V. V. Vlasov, “On the solvability and properties of solutions of functional-differential equations in a Hilbert space,” Sb. Math., 186, No. 8, 1147–1172 (1995).
V. V. Vlasov, “On the solvability and estimates for the solutions of functional-differential equations in Sobolev spaces,” Proc. Steklov Inst. Math., 4(227), 104–115 (1999).
M. A. Vorontsov, N. G. Iroshnikov, and R. L. Abernathy, “Diffractive patterns in a nonlinear optical two-dimensional feedback system with field rotation,” Chaos Solitons Fractals, 4, No. 8–9, 1701–1716 (1994).
Author information
Authors and Affiliations
Corresponding author
Additional information
__________
Translated from Sovremennaya Matematika. Fundamental’nye Napravleniya (Contemporary Mathematics. Fundamental Directions), Vol. 21, Proceedings of the Seminar on Differential and Functional Differential Equations Supervised by A. Skubachevskii (Peoples’ Friendship University of Russia), 2007.
Rights and permissions
About this article
Cite this article
Selitskii, A.M. The third boundary-value problem for parabolic differential-difference equations. J Math Sci 153, 591–611 (2008). https://doi.org/10.1007/s10958-008-9138-8
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-008-9138-8