Description

• Title:
  A diffusive logistic equation with U-shaped density dependent dispersal on the boundary
• Creator:
  Goddard II, Jerome;
  Morris, Quinn;
  Payne, Catherine;
  Shivaji, Ratnasingham
• Description:
  We study positive solutions to the steady state reaction diffusion equation: \begin{equation*} \begin{cases} - \Delta v = \lambda v(1-v), & x \in \Omega_0, \\ \displaystyle \frac{\partial v}{\partial \eta} + \gamma \sqrt{\lambda} ( v-A)^2 v =0 , & x \in \partial \Omega_0, \end{cases} \end{equation*} where $\Omega_0$ is a bounded domain in $\mathbb{R}^n$; $n \ge 1$ with smooth boundary $\partial \Omega_0$, ${\partial }/{\partial \eta}$ is the outward normal derivative, $A \in (0,1)$ is a constant, and $\lambda$, $\gamma$ are positive parameters. Such models arise in the study of population dynamics when the population exhibits a U-shaped density dependent dispersal on the boundary of the habitat. We establish existence, multiplicity, and uniqueness results for certain ranges of the parameters $\lambda$ and $\gamma$. We obtain our existence and mulitplicity results via the method of sub-super solutions.
• Object availability:
  free access
• Rights:
  Prawa autorskie (c) 2019 Topological Methods in Nonlinear Analysis
• Date:
  2019.01.12
• Type:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Language:
  English
• Source:
  Topological Methods in Nonlinear Analysis; Vol 53, No 1 (March 2019); 335 - 349;
  1230-3429
• Publisher:
  Nicolaus Copernicus University in Toruń
• Relation: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.047/16621 ;https://apcz.umk.pl/TMNA/article/view/TMNA.2018.047/16622
• Subject:
  Mathematical biology;
  reaction diffusion model;
  nonlinear boundary conditions;
  U-shaped density dependent dispersal;
  35J25;
  35J66
• Identifier: https://apcz.umk.pl/TMNA/article/view/TMNA.2018.047
• Data provider:
  Akademicka Platforma Czasopism
• Can I use it?:
  seek permission
• Type:
  other