Description

• Tytuł:
  Positive solutions with a singular set for semilinear parabolic equations
• Twórca:
  Jah, Sidi Hamidou;
  Riahi, Lotfi
• Opis:
  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 $E$.
• Dostępność obiektu:
  free access
• Prawa: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2025 Sidi Hamidou Jah, Lotfi Riahi
• Data:
  2025.03.31
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  English
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 65, No 1 (March 2025); 265 - 285;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/60418/42255 ;https://apcz.umk.pl/TMNA/article/view/60418/42256
• Temat i słowa kluczowe:
  Partial differential equations;
  semilinear parabolic equation;
  semilinear elliptic equation;
  Dirichlet boundary condition;
  positive solution;
  singular solution;
  Kato class;
  asymptotic behavior;
  35K58, 35B40, 35J61
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/60418
• Dostawca danych:
  Akademicka Platforma Czasopism
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