Dynamics for nonlocal diffusion problems with a free boundary and a fixed boundary
arXiv:2105.13056
Abstract
In this paper, we first consider two scalar nonlocal diffusion problems with a free boundary and a fixed boundary. We obtain the global existence, uniqueness and longtime behaviour of solution of these two problems. The spreading-vanishing dichotomy and sharp criteria for spreading and vanishing are established. We also prove that accelerated spreading could happen if and only if a threshold condition is violated by kernel function. Then we discuss a classical Lotka-Volterra predator-prey model with nonlocal diffusions and a free boundary which can be seen as nonlocal diffusion counterpart of the model in the work of Wang (2014 J. Differential Equations \textbf{256}, 3365-3394).
arXiv comment33 pages
References in corpus (4)
- Two species nonlocal diffusion systems with free boundaries
- Semi-wave, traveling wave and spreading speed for monostable cooperative systems with nonlocal diffusion and free boundaries
- Approximation of random diffusion equation by nonlocal diffusion equation in free boundary problems of one space dimension
- The high dimensional Fisher-KPP nonlocal diffusion equation with free boundary and radial symmetry