Abstract
Conditions for stabilization of solution of Cauchy problem for a linear second-order parabolic equation in nondivergent form are studied.
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References
V. N. Denisov, “On behavior if solutions of parabolic equation for large values of time,” Usp. Mat. Nauk, 60, No. 4, 145–212 (2005).
V. N. Denisov, “On stabilization of solution of Cauchy problem for a parabolic equation with lower coefficient, Fundam. Prikl. Mat.,, 12, No. 4, 79–97 (2006).
V. N. Denisov, “On stabilization of solution of Cauchy problem for a nondivergent parabolic equation with lower coefficient in classes of growing initial functions,” Dokl. Ross. Akad. Nauk, 430, No. 5, 586–588 (2010).
V. N. Denisov, “Stabilization of solution of Cauchy problem for a nondivergent parabolic equation with growing lower coefficients,” Trudy Mat. Inst. Akad. Nauk SSSR, 270, 97–109 (2010).
V. N. Denisov, “A sufficient conditions for stabilization of solution of Cauchy problem for a nondivergent parabolic equation with lower coefficients,” Sovrem. Mat. Fundam. Napravleniya, 36, 61–71 (2010).
V. N. Denisov, “On necessary and sufficient conditions for stabilization of solution of Cauchy problem for a parabolic equation with lower coefficients,” Dokl. Ross. Akad. Nauk, 433, No. 4, 452–454 (2010).
M. V. Fedoryuk, Ordinary Differential Equations [in Russian], Nauka, Moscow (1983).
A. Friedman, Partial Differential Equations of Parabolic Type [Russian translation], Mir, Moscow (1968).
D. Gilbarg and N. Trudinger, Elliptic Second-Order Partial Differential Equations [Russian translation], Nauka, Moscow (1989).
G. Hardy, Divergent Series [Russian translation], Faktorial Press, Moscow (2006).
A. M. Il’in, A. S. Kalashnikov, and O. A. Oleinik, “Linear second-order equations of parabolic type,” Usp. Mat. Nauk, 17, No. 3, 3–146 (1962).
V. A. Il’in, V. A. Sadovnichii, and Bl. Kh. Sendov, Mathematical Analysis [in Russian], Pts.1,2, MGU, Moscow (2005).
E. L. Ince, Ordinary Differential Equations [Russian translation], Faktorial Press, Moscow (2005).
G. V. Smirnova, “Cauchy problem for parabolic equations degenerating at infinity,” Mat. Sb., 70, No. 4, 591–604 (1966).
E. Stein and G. Weiss, Introduction to Harmonic Analysis in Non-Euclidean Spaces [Russian translation], Mir, Moscow (1974).
G. N. Watson, Theory of Bessel Functions [Russian translation], IL, Moscow (1949).
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Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 78, Partial Differential Equations and Optimal Control, 2012.
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Denisov, V.N. Stabilization of solution of cauchy problem for a non-divergent parabolic equation. J Math Sci 189, 188–222 (2013). https://doi.org/10.1007/s10958-013-1181-4
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DOI: https://doi.org/10.1007/s10958-013-1181-4