Description

• Title:
  Positive solutions with a singular set for semilinear parabolic equations
• Creator:
  Jah, Sidi Hamidou;
  Riahi, Lotfi
• Description:
  We study the existence and large time behavior of positive solutions for the semilinear parabolic equation $\frac{\partial u}{\partial t}(x,t) =\Delta u(x,t)+ V(x)u(x,t) +f(x,u(x,t))$ with initial Dirichlet boundary conditions on $(D\setminus E)\times (0,\infty)$, where $D$ is a bounded Lipschitz domain in $\mathbb{R}^n$, $ n\geq 3$, $E$ is a prescribed compact set of $D$, and $V$ and $f$ are real-valued functions satisfying some general conditions. Our results cover various types of nonlinearities and extend known results proved for the power nonlinearity $f(x,u)=W(x)u^p$ and a singular one-point set $E$.
• Object availability:
  free access
• Rights: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2025 Sidi Hamidou Jah, Lotfi Riahi
• Date:
  2025.03.31
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 65, No 1 (March 2025); 265 - 285;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/60418/42255 ;https://apcz.umk.pl/TMNA/article/view/60418/42256
• Subject:
  Partial differential equations;
  semilinear parabolic equation;
  semilinear elliptic equation;
  Dirichlet boundary condition;
  positive solution;
  singular solution;
  Kato class;
  asymptotic behavior;
  35K58, 35B40, 35J61
• Identifier: https://apcz.umk.pl/TMNA/article/view/60418
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other