Nonlocal evolution equations with p[u(x, t)]-Laplacian and lower-order terms

Nonlocal evolution equations with p[u(x, t)]-Laplacian and lower-order terms Full article

Journal

Journal of Elliptic and Parabolic Equations
ISSN: 2296-9020

Output data

Year: 2020, Volume: 6, Number: 1, Pages: 211-237 Pages count : 27 DOI: 10.1007/s41808-020-00065-x

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	CMAF‑CIO, University of Lisbon
4	Mathematics Department, University of Oviedo

We study the homogeneous Dirichlet problem for a class of nonlocal singular parabolic equations ut-div(|∇u|p[u]-2∇u)=f((x,t),u,l(u))inQT=Ω×(0,T),where Ω⊂ Rd, d≥ 2, is a smooth domain, p[u] = p(l(u)) is a given function with values in the interval [p-,p+]⊂(2dd+2,2), and l(u)=∫Ω|u(x,t)|αdx, α∈ [1, 2], is a functional of the unknown solution. We prove the existence of a strong solution such that ut∈L2(QT),u∈L∞(0,T;W01,2(Ω)),|Dij2u|p[u]∈L1(QT).Conditions of uniqueness of strong solutions are obtained

Antontsev S. , Shmarev S.
Nonlocal evolution equations with p[u(x, t)]-Laplacian and lower-order terms
Journal of Elliptic and Parabolic Equations. 2020. V.6. N1. P.211-237. DOI: 10.1007/s41808-020-00065-x WOS Scopus РИНЦ OpenAlex

Web of science:	WOS:000528646900001
Scopus:	2-s2.0-85084121184
Elibrary:	43303743
OpenAlex:	W3019924449

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Scopus	4
OpenAlex	4
Elibrary	4
Web of science	3