Diwen Chang

On the well-posedness of porous medium equations on general metric measure spaces

On general metric measure spaces, we develop a new well-posedness theory for the signed porous medium equation and its fast diffusion counterpart \[ \partial_t u = \mathcal{L}\left(|u|^{m-1}u\right), \qquad m>0, \] where $\mathcal{L}$ is the associated non-positive self-adjoint operator of a symmetric Dirichlet form. T...