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 Mat. Sb. (N.S.), 1982, Volume 117(159), Number 3, Pages 359–378 (Mi msb2213)

This article is cited in 5 scientific papers (total in 5 papers)

Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations

S. B. Kuksin

Abstract: This paper considers a boundary value problem for a quasilinear parabolic equation. In terms of Sobolev and Besov spaces the author determines a solution space $A$ and a space $B$ of initial conditions and right hand members such that the operator corresponding to the boundary value problem is a diffeomorphism, analytic in the Frechet sense, of the whole space $A$ and a domain $\mathscr O$ in the space $B$. The behavior of the inverse operator of the problem around the boundary of $\mathscr O$ is studied, and it is shown that for different problems the domain $\mathscr O$ can coincide with the whole function space or be a strict subset of it.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Sbornik, 1983, 45:3, 359–378

Bibliographic databases:

UDC: 517.946
MSC: 35K55, 46E35, 46E15, 58C20
Received: 04.02.1981

Citation: S. B. Kuksin, “Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations”, Mat. Sb. (N.S.), 117(159):3 (1982), 359–378; Math. USSR-Sb., 45:3 (1983), 359–378

Citation in format AMSBIB
\Bibitem{Kuk82} \by S.~B.~Kuksin \paper Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations \jour Mat. Sb. (N.S.) \yr 1982 \vol 117(159) \issue 3 \pages 359--378 \mathnet{http://mi.mathnet.ru/msb2213} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=648413} \zmath{https://zbmath.org/?q=an:0549.35067|0501.35046} \transl \jour Math. USSR-Sb. \yr 1983 \vol 45 \issue 3 \pages 359--378 \crossref{https://doi.org/10.1070/SM1983v045n03ABEH001012} 

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Citing articles on Google Scholar: Russian citations, English citations
Related articles on Google Scholar: Russian articles, English articles

This publication is cited in the following articles:
1. Galaktionov V., Kurdyumov S., Samarskii A., “A Parabolic-System of Quasilinear Equations .1.”, Differ. Equ., 19:12 (1983), 1558–1574
2. D. A. Khrychev, “On approximate solution of systems of moment equations”, Math. USSR-Sb., 54:1 (1986), 81–98
3. D. A. Khrychev, “Moments of solutions of evolution equations and suboptimal programmed controls”, Sb. Math., 198:7 (2007), 1025–1062
4. Shirikyan A., “Qualitative Properties of Stationary Measures for Three-Dimensional Navier–Stokes Equations”, J. Funct. Anal., 249:2 (2007), 284–306
5. Agrachev A., Kuksin S., Sarychev A., Shirikyan A., “On Finite-Dimensional Projections of Distributions for Solutions of Randomly Forced 2D Navier–Stokes Equations”, Ann. Inst. Henri Poincare-Probab. Stat., 43:4 (2007), 399–415
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