Opis

• Tytuł:
  Asymptotic dynamics of non-autonomous fractional reaction-diffusion equations on bounded domains
• Twórca:
  Li, Xin;
  Shen, Wenxian;
  Sun, Chunyou
• Opis:
  In this paper, we consider the asymptotic dynamics of non-autonomous fractional reaction-diffusion equations of the form \[u_{t}+(-\Delta)^{s}u+f(u)=g(t)\] complemented with the Dirichlet boundary condition on a bounded domain. First, we obtain some higher-attraction results for pullback attractors, that is, without any additional $t$-differentiability assumption on the forcing term $g$, for any space dimension $N$ and any growth power $p\geq2$ of $f$, the known $(L^{2}(\Omega), L^{2}(\Omega))$ pullback attractor can indeed attract every $L^{2}(\Omega)$-bounded set in the $L^{2+\delta}(\Omega)$-norm for every $\delta\in [0,\infty)$ as well as in the $W_{0}^{s,2}(\Omega)$-norm. Then, we construct a family of Borel probability measures $\{\mu_{t}\}_{t\in\mathbb{R}}$, whose supports satisfy the higher-attraction results. Finally, we investigate the relationship between such the Borel probability measures and time-dependent statistical solutions for this fractional Laplacian equation.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa:
  Prawa autorskie (c) 2020 Topological Methods in Nonlinear Analysis
• Data:
  2020.01.19
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 55, No 1 (March 2020); 105 - 139;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.063/24524 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2019.063/24525
• Temat i słowa kluczowe:
  Non-autonomous;
  fractional Laplacian;
  pullback attractor;
  pullback attraction;
  generalized Banach limit;
  time-dependent statistical solutions;
  35B40;
  35B41;
  35R11;
  37L40;
  76D06
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/TMNA.2019.063
• Dostawca danych:
  Akademicka Platforma Czasopism
• Czy mogę z tego obiektu skorzystać?:
  poproś o pozwolenie
• Rodzaj zawartości:
  pozostałe