This article is cited in 2 scientific papers (total in 2 papers)
On global solvability of nonlinear parabolic boundary-value problems
A. V. Babin
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 $T$).
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Mathematics of the USSR-Sbornik, 1975, 26:1, 89–104
MSC: 35K55, 35K35
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
\paper On~global solvability of nonlinear parabolic boundary-value problems
\jour Mat. Sb. (N.S.)
\jour Math. USSR-Sb.
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This publication is cited in the following articles:
S. B. Kuksin, “On quasilinear parabolic equations”, Russian Math. Surveys, 35:4 (1980), 173–174
S. B. Kuksin, “Diffeomorphisms of function spaces corresponding to quasilinear parabolic equations”, Math. USSR-Sb., 45:3 (1983), 359–378
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