On a class of fully nonlinear parabolic equations Full article
| Journal |
Advances in Nonlinear Analysis
ISSN: 2191-9496 |
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| Output data | Year: 2019, Volume: 8, Number: 1, Pages: 79-100 Pages count : 22 DOI: 10.1515/anona-2016-0055 | ||||||
| Tags | asymptotic behavior; extinction in a finite time; Fully nonlinear parabolic equation; strong solution | ||||||
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Abstract:
We study the homogeneous Dirichlet problem for the fully nonlinear equation (equation presented) with the parameters m > 1, σ > 1 and d ≥ 0. At the points where δu = 0, the equation degenerates if m > 2, or becomes singular if m (1, 2).We derive conditions of existence and uniqueness of strong solutions, and study the asymptotic behavior of strong solutions as t → ∞. Sufficient conditions for exponential or power decay of ∥∇u(t)∥ 2,ω are derived. It is proved that for certain ranges of the exponents m and σ, every strong solution vanishes in a finite time.
Cite:
Antontsev S.
, Shmarev S.
On a class of fully nonlinear parabolic equations
Advances in Nonlinear Analysis. 2019. V.8. N1. P.79-100. DOI: 10.1515/anona-2016-0055 WOS Scopus РИНЦ OpenAlex
On a class of fully nonlinear parabolic equations
Advances in Nonlinear Analysis. 2019. V.8. N1. P.79-100. DOI: 10.1515/anona-2016-0055 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000459891200005 |
| Scopus: | 2-s2.0-85062615787 |
| Elibrary: | 38697369 |
| OpenAlex: | W2552389028 |