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This article is cited in 18 scientific papers (total in 18 papers)
$L_1$–$L_\infty$ estimates of solutions of the Cauchy
problem for an anisotropic degenerate parabolic equation with double
non-linearity and growing initial data
S. P. Degtyarev, A. F. Tedeev Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences
Abstract:
The Cauchy
problem for a degenerate parabolic equation with
anisotropic $p$-Laplacian and double
non-linearity is considered.
For increasing initial data local estimates for the
$L_\infty$-norm of a solution are obtained, which
yield a precise characterization of the growth of solutions at
infinity. An estimate for the order of the length of the time
interval on which a solution
is defined is found in its dependence on the initial data.
Bibliography: 12 titles.
Received: 10.04.2006 and 15.12.2006
Citation:
S. P. Degtyarev, A. F. Tedeev, “$L_1$–$L_\infty$ estimates of solutions of the Cauchy
problem for an anisotropic degenerate parabolic equation with double
non-linearity and growing initial data”, Mat. Sb., 198:5 (2007), 45–66; Sb. Math., 198:5 (2007), 639–660
Linking options:
https://www.mathnet.ru/eng/sm1556https://doi.org/10.1070/SM2007v198n05ABEH003853 https://www.mathnet.ru/eng/sm/v198/i5/p45
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Abstract page: | 628 | Russian version PDF: | 250 | English version PDF: | 22 | References: | 66 | First page: | 7 |
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