Date/Time Date(s) - 10/04/20261:30 pm - 2:30 pm
Speaker: Chu Chu (York University)
Location: Hamilton Hall, Room 410
Title: Well-posedness of the Fisher–KPP equation with Neumann, Dirichlet, and Robin boundary conditions on the real half line.
Abstract: In this paper, we study the well-posedness of the classical solution of the Fisher-KPP equation under Neumann, Dirichlet, and Robin boundary conditions by considering a general functional form $f(u)$. We approximate the entire solutions of Neumann, Dirichlet, and Robin boundary conditions to positive odd stationary solutions, which are equivalent to positive odd steady-state solutions. In a condition of $L^{\infty}$ space defined on a real half-line, which means they are equal to each other almost everywhere. However, they are equal everywhere according to continuous properties of classical solutions. We claim and show the stability of the Fisher-KPP equation in each boundary condition. Since the steady-state solution is equal to 0 or 1, taking into account the nonlinear term, we obtain that the nonlinear term is equal to 0. Then we are able to solve the nonlinear equation, which is equivalent to solving a linear diffusion equation by separation of variables and also uniqueness. Finally, we conclude that the Fisher-KPP equation for each boundary condition is well-posed only for positive odd stationary solutions.