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 Mat. Sb. (N.S.), 1975, Volume 97(139), Number 1(5), Pages 94–109 (Mi msb3489)

On global solvability of nonlinear parabolic boundary-value problems

A. V. Babin

Abstract: In this paper one considers nonlinear parabolic boundary-value problems of a general form. It is known that the solution of such problems can go to infinity in a finite interval of time. One shows that this effect is in a certain sense of a finite-dimensional character. Namely, one shows that if the solution is considered on the segment $[0,T]$, while the right-hand sides are bounded in the norm by a constant $R$ and satisfy a finite number of conditions, then the problem admits a solution which is smooth for $0\leqslant t\leqslant T$ (the number of conditions depends on $R$ and $T$).
Bibliography: 11 titles.

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English version:
Mathematics of the USSR-Sbornik, 1975, 26:1, 89–104

Bibliographic databases:

UDC: 517.946.9
MSC: 35K55, 35K35

Citation: A. V. Babin, “On global solvability of nonlinear parabolic boundary-value problems”, Mat. Sb. (N.S.), 97(139):1(5) (1975), 94–109; Math. USSR-Sb., 26:1 (1975), 89–104

Citation in format AMSBIB
\Bibitem{Bab75} \by A.~V.~Babin \paper On~global solvability of nonlinear parabolic boundary-value problems \jour Mat. Sb. (N.S.) \yr 1975 \vol 97(139) \issue 1(5) \pages 94--109 \mathnet{http://mi.mathnet.ru/msb3489} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=385327} \zmath{https://zbmath.org/?q=an:0323.35048} \transl \jour Math. USSR-Sb. \yr 1975 \vol 26 \issue 1 \pages 89--104 \crossref{https://doi.org/10.1070/SM1975v026n01ABEH002471} 

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This publication is cited in the following articles:
1. S. B. Kuksin, “On quasilinear parabolic equations”, Russian Math. Surveys, 35:4 (1980), 173–174
2. S. B. Kuksin, “Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations”, Math. USSR-Sb., 45:3 (1983), 359–378
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