Positivity and asymptotic behaviour of solutions to a generalized
nonlocal fast diffusion equation
Positivity and asymptotic behaviour of solutions to a generalized
nonlocal fast diffusion equation
We study the positivity and asymptotic behaviour of nonnegative solutions of a general nonlocal fast diffusion equation, \[\partial_t u + \mathcal{L}\varphi(u) = 0,\] and the interplay between these two properties. Here $\mathcal{L}$ is a stable-like operator and $\varphi$ is a singular nonlinearity. We start by analysing positivity by means of …