On a class of nonlocal evolution equations with the p[∇u]-Laplace operator Full article
| Journal |
Journal of Mathematical Analysis and Applications
ISSN: 0022-247X |
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| Output data | Year: 2021, Volume: 501, Number: 2, Pages: 125221 Pages count : 1 DOI: 10.1016/j.jmaa.2021.125221 | ||||||||
| Tags | Nonlocal evolution equations; Singular parabolic equation; Variable nonlinearity | ||||||||
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Abstract:
We study the homogeneous Dirichlet problem for the class of singular parabolic equations ut−div(|∇u|p[∇u]−2∇u)=fin Ω×(0,T), where Ω⊂Rd, d≥2, is a smooth domain. The exponent p nonlocally depends on the gradient of the solution: p is a given function defined by p[∇u]≡p(l(|∇u|)),l(|s|)=∫Ω|s|αdx with a constant α∈(1,2]. We find sufficient conditions on the data that guarantee global in time existence and uniqueness of a strong solution of the problem. It is shown that the problem has a solution if either u0 and f, or p′(s) are sufficiently small.
Cite:
Antontsev S.
, Kuznetsov I.
, Shmarev S.
On a class of nonlocal evolution equations with the p[∇u]-Laplace operator
Journal of Mathematical Analysis and Applications. 2021. V.501. N2. P.125221. DOI: 10.1016/j.jmaa.2021.125221 WOS Scopus РИНЦ OpenAlex
On a class of nonlocal evolution equations with the p[∇u]-Laplace operator
Journal of Mathematical Analysis and Applications. 2021. V.501. N2. P.125221. DOI: 10.1016/j.jmaa.2021.125221 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000653644000019 |
| Scopus: | 2-s2.0-85103697728 |
| Elibrary: | 46779418 |
| OpenAlex: | W3142450580 |