Traveling waves in semilinear parabolic equations with applications to voting models and population dynamics

The talk is devoted to the study of traveling waves for a semilinear parabolic equation, the nonlinear term of which can have both a local and a non-local character. This is primarily the equation considered in the seminal work of Kolmogorov, Petrovskii and Piskunov. We consider a class of nonlinearities that arise in connection with the development of applications in voting models based on branching Brownian motion. We present an analytical solution that generalizes the results of Ablowitz and Kaliappan to a broader class of equations. The method of constructing exact solutions also applies to the nonlocal modification of the KPP equation that arises from population dynamics.

The talk will be streamed through “Kontur Talk”: https://mian.ktalk.ru/xr9pf6k3br12?pinCode=2494