Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations
Texas State University, Department of Mathematics
We consider a reaction-diffusion equation with nonlocal anisotropic diffusion and a linear combination of local and nonlocal monostable-type reactions in a space of bounded functions on Rd. Using the properties of the corresponding semiflow, we prove the existence of monotone traveling waves along those directions where the diffusion kernel is exponentially integrable. Among other properties, we prove continuity, strict monotonicity and exponential integrability of the traveling wave profiles.
Nonlocal diffusion, Reaction-diffusion equation, Fisher-KPP equation, Traveling waves, Nonlocal nonlinearity, Anisotropic kernels, Integral equation
Finkelshtein, D., Kondratiev, Y., & Tkachov, P. (2019). Existence and properties of traveling waves for doubly nonlocal Fisher-KPP equations. <i>Electronic Journal of Differential Equations, 2019</i>(10), pp. 1-27.