A Note on the formulation of the Neumann boundary condition for a nonlocal problem

Antonio Luiz Pereira

The nonlocal diffusion equation \begin{equation*} \begin{cases} u_t(t,x) & = \int_Ω K(x,y) \, u(t,y) \, d\,y - \int_Ω K(y,x) \, u(t,x) \, d \, y u(0,x) & = u_0(x) \end{cases} \end{…