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Mat. Sb. (N.S.), 1985, Volume 128(170), Number 2(10), Pages 147–168 (Mi msb2121)  

This article is cited in 17 scientific papers (total in 17 papers)

On uniform stabilization of the solution of the second mixed problem for a second order parabolic equation

A. K. Gushchin, V. P. Mikhailov, Yu. A. Mikhailov

Abstract: 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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English version:
Mathematics of the USSR-Sbornik, 1987, 56:1, 141–162

Bibliographic databases:

UDC: 517.9
MSC: 35K20, 35B40
Received: 18.03.1985

Citation: 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”, Mat. Sb. (N.S.), 128(170):2(10) (1985), 147–168; Math. USSR-Sb., 56:1 (1987), 141–162

Citation in format AMSBIB
\by A.~K.~Gushchin, V.~P.~Mikhailov, Yu.~A.~Mikhailov
\paper On uniform stabilization of the solution of the second mixed problem for a~second order parabolic equation
\jour Mat. Sb. (N.S.)
\yr 1985
\vol 128(170)
\issue 2(10)
\pages 147--168
\jour Math. USSR-Sb.
\yr 1987
\vol 56
\issue 1
\pages 141--162

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    This publication is cited in the following articles:
    1. Yu. A. Mikhailov, “On uniform quasistabilization of solutions of the second mixed problem for a second-order hyperbolic equation”, Math. USSR-Sb., 57:1 (1987), 243–262  mathnet  crossref  mathscinet  zmath
    2. A. K. Gushchin, V. P. Mikhailov, “On uniform quasiasymptotics of solutions of the second mixed problem for a hyperbolic equation”, Math. USSR-Sb., 59:2 (1988), 409–427  mathnet  crossref  mathscinet  zmath
    3. A. K. Gushchin, V. P. Mikhailov, “Comparison theorems for solutions of hyperbolic equations”, Math. USSR-Sb., 62:2 (1989), 349–371  mathnet  crossref  mathscinet  zmath
    4. Lezhnev A., “Bounds of Green-Function and Solutions of a 2nd Mixed Problem for a Parabolic Equation”, Differ. Equ., 25:4 (1989), 478–486  mathnet  mathscinet  zmath  isi
    5. V. V. Zhikov, “Asymptotic problems connected with the heat equation in perforated domains”, Math. USSR-Sb., 71:1 (1992), 125–147  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. F. Kh. Mukminov, “On uniform stabilization of solutions of the first mixed problem for a parabolic equation”, Math. USSR-Sb., 71:2 (1992), 331–353  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    7. A. A. Grigor'yan, “The heat equation on noncompact Riemannian manifolds”, Math. USSR-Sb., 72:1 (1992), 47–77  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    8. F. Kh. Mukminov, “On uniform stabilization of solutions of the exterior problem for the Navier–Stokes equations”, Russian Acad. Sci. Sb. Math., 81:2 (1995), 297–320  mathnet  crossref  mathscinet  zmath  isi
    9. L. M. Kozhevnikova, F. Kh. Mukminov, “Estimates of the stabilization rate as $t\to\infty$ of solutions of the first mixed problem for a quasilinear system of second-order parabolic equations”, Sb. Math., 191:2 (2000), 235–273  mathnet  crossref  crossref  mathscinet  zmath  isi
    10. F. Kh. Mukminov, I. M. Bikkulov, “Stabilization of the norm of the solution of a mixed problem in an unbounded domain for parabolic equations of orders 4 and 6”, Sb. Math., 195:3 (2004), 413–440  mathnet  crossref  crossref  mathscinet  zmath  isi
    11. V. N. Denisov, “On the behaviour of solutions of parabolic equations for large values of time”, Russian Math. Surveys, 60:4 (2005), 721–790  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    12. Grigor'yan A., “Heat Kernels on Weighted Manifolds and Applications”, Ubiquitous Heat Kernel, Contemporary Mathematics Series, 398, ed. Jorgenson J. Walling L., Amer Mathematical Soc, 2006, 93–191  crossref  mathscinet  zmath  isi
    13. A. V. Lezhnev, “Ob odnoi teoreme vlozheniya dlya funktsii s summiruemym gradientom”, Trudy sedmoi Vserossiiskoi nauchnoi konferentsii s mezhdunarodnym uchastiem (3–6 iyunya 2010 g.). Chast 3, Differentsialnye uravneniya i kraevye zadachi, Matem. modelirovanie i kraev. zadachi, Samarskii gosudarstvennyi tekhnicheskii universitet, Samara, 2010, 149–152  mathnet
    14. Grigor'yan A. Telcs A., “Two-Sided Estimates of Heat Kernels on Metric Measure Spaces”, Ann. Probab., 40:3 (2012), 1212–1284  crossref  mathscinet  zmath  isi
    15. Manuel Núñez, “On the one-dimensional relativistic induction equation”, Math. Meth. Appl. Sci, 2013, n/a  crossref
    16. A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov, “Slowly varying on infinity semigroups of operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 1–10  mathnet  crossref
    17. A. V. Pskhu, “O stabilizatsii reshenii zadachi Koshi dlya drobnogo diffuzionno-volnovogo uravneniya”, Materialy mezhdunarodnoi nauchnoi konferentsii Aktualnye problemy prikladnoi matematiki i fiziki Kabardino-Balkariya, Nalchik, 1721 maya 2017 g., Itogi nauki i tekhn. Ser. Sovrem. mat. i ee pril. Temat. obz., 149, VINITI RAN, M., 2018, 84–94  mathnet  mathscinet
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