On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator

On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator Full article

Journal

Nonlinear Analysis: Real World Applications
ISSN: 1468-1218

Output data

Year: 2020, Volume: 56, Pages: 103165 Pages count : 1 DOI: 10.1016/j.nonrwa.2020.103165

Tags

Nonlocal equation; Singular parabolic equation; Strong solutions; Variable nonlinearity

Authors

Antontsev Stanislav ^1,2,3 , Shmarev Sergey ⁴

Affiliations

1	Lavrentyev Institute of Hydrodynamics of SB RAS, Novosibirsk, Russia
2	Novosibirsk State University, Novosibirsk, Russia
3	University of Lisbon
4	Mathematics Department, University of Oviedo, c/Fededrico García Lorca, 18, 33007 Oviedo, Spain

We study the homogeneous Dirichlet problem for a class of nonlocal singular parabolic equations ut−div|∇u|p[u]−2∇u=fin Ω×(0,T),where Ω⊂Rd, d≥2, is a smooth bounded domain, p[u]=p(l(u)) is a given function with values in the interval [p−,p+]⊂(1,2), and l(u)=∫Ω|u(x,t)|αdx, α∈[1,2], is a functional of the unknown solution. We find sufficient conditions for global or local in time solvability of the problem, prove the uniqueness, and show that every solution gets extinct in a finite time.

Antontsev S. , Shmarev S.
On a class of nonlocal evolution equations with the p[u(x,t)]-Laplace operator
Nonlinear Analysis: Real World Applications. 2020. V.56. P.103165. DOI: 10.1016/j.nonrwa.2020.103165 WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000549179500013
Scopus:	2-s2.0-85085732253
Elibrary:	43291725
OpenAlex:	W3032971296

DB	Citing
Scopus	8
OpenAlex	8
Elibrary	8
Web of science	7