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

Stanislav Antontsev, Sergey Shmarev

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)211-237
Number of pages27
JournalJournal of Elliptic and Parabolic Equations
Volume6
Issue number1
DOIs
Publication statusPublished - 1 Jun 2020

Keywords

  • Nonlocal equation
  • Singular parabolic equation
  • Strong solutions
  • Variable nonlinearity
  • P(U)-LAPLACIAN
  • VARIABLE EXPONENT
  • UNIQUENESS

OECD FOS+WOS

  • 1.01 MATHEMATICS

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