Tkachov, Pasha: Front propagation in the non-local Fisher-KPP equation. 2017
Inhalt
- Introduction
- Existence, uniqueness, and boundedness
- Around the comparison principle
- Traveling waves
- Existence and properties of traveling waves
- Speed and profile of a traveling wave
- Uniqueness of traveling waves
- Front propagation with a constant speed
- Long-time behavior along a direction
- Global long-time behavior
- Proof of Theorem 5.10
- Fast propagation for slow decaying dispersal kernels
- Accelerating front propagation
- Technical tools
- Level sets for heavy tailed functions on R
- Examples
- Class 1: l(s)Dlogs, s, D>0
- Class 2: l(s)D(logs)q, s, q>1, D>0
- Class 3: l(s)s, (0,1)
- Class 4: l(s) repstopdfs(logs), >1
- Technical tools on Rd
- Domain of uniform convergence to positive constant solution
- Domain of uniform convergence to zero solution
- Corollaries and examples
- Pictures