Geodesic
On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation
Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 141-162 Cet article a éte moissonné depuis la source Math-Net.Ru

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The authors investigate uniform stabilization of the solution of the second mixed problem in a cylindrical domain $(t>0)\times\Omega$ for a linear parabolic equation of second order. For a rather broad class of unbounded domains $\Omega\subset\mathbf R_n$ a sharp estimate of the Green function for the problem in question is established, and a condition on the initial function is found which is necessary and sufficient for uniform stabilization of the solution. Bibliography: 14 titles. 
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A. K. Gushchin; V. P. Mikhailov; Yu. A. Mikhailov. On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation. Sbornik. Mathematics, Tome 56 (1987) no. 1, pp. 141-162. http://geodesic.mathdoc.fr/item/SM_1987_56_1_a9/

[1] Zhikov V. V., “O stabilizatsii reshenii parabolicheskikh uravnenii”, Matem. sb., 104(146) (1977), 597–616 | Zbl

[2] Kamin S., “On stabilization of solutions of the Cauchy problem for parabolic equations”, Proc. Roy. Soc. Edinburgh, Sect. A, 76:1 (1976), 43–53 | MR | Zbl

[3] Moser J., “A Harnack's inequality for parabolic differential equations”, Comm. Pure and Appl. Math., 17:101–134 (1964) | MR | Zbl

[4] Guschin A. K., “O ravnomernoi stabilizatsii reshenii vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 119(161) (1982), 451–508

[5] Nash J., “Continuity of solutions of parabolic and elliptic equations”, Amer. J. Math., 80 (1958), 931–954 | DOI | MR | Zbl

[6] Guschin A. K., “Ob otsenkakh reshenii kraevykh zadach dlya parabolicheskogo uravneniya vtorogo poryadka”, Tr. MIAN, CXXVI (1973), 5–45

[7] Guščin A. K., “On the behaviour as $t\to\infty$ of solutions of the second mixed problem for a second – order parabolic equation”, Appl. Math. Optim., 6 (1980), 169–180 | DOI | MR

[8] Guschin A. K., “Ob otsenke integrala Dirikhle”, Matem sb., 99(141) (1976), 282–294 | Zbl

[9] Guschin A. K., “Stabilizatsiya resheniya vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka”, Matem. sb., 101(143) (1976), 459–499 | Zbl

[10] Eidelman S. D, Parabolicheskie sistemy, Nauka, M., 1964 | MR | Zbl

[11] Ladyzhenskaya O. A., Solonnikov V. A., Uraltseva N. N., Lineinye i kvazilineinye uravneniya parabolicheskogo tipa, Nauka, M., 1967

[12] Guschin A. K., “Nekotorye svoistva obobschennogo resheniya vtoroi smeshannoi zadachi dlya parabolicheskogo uravneniya”, Matem. sb., 97(139) (1975), 242–261 | Zbl

[13] De Giorgi E., “Sulla differenziabilità e 1'analiticità delle estremali degli integrali multipli regolari”, Mem. Accad. Sci. Torino, ser. 3, 1957, no. 3, 25–43 ; Математика, 4:6 (1960), 23–38 | MR | Zbl

[14] Ushakov V. I., “Stabilizatsiya reshenii tretei smeshannoi zadachi dlya parabolicheskogo uravneniya vtorogo poryadka v netsilindricheskoi oblasti”, Matem. sb., 111(153) (1980), 95–115 | MR | Zbl