Now showing items 1-4 of 4

• #### Asymptotic behaviour for fractional diffusion-convection equations ﻿

(2017-10)
We consider a convection-diffusion model with linear fractional diffusion in the sub-critical range. We prove that the large time asymptotic behavior of the solution is given by the unique entropy solution of the convective ...
• #### Existence of weak solutions for a general porous medium equation with nonlocal pressure ﻿

(submitted, 2017-10)
We study the general nonlinear diffusion equation $u_t=\nabla\cdot (u^{m-1}\nabla (-\Delta)^{-s}u)$ that describes a flow through a porous medium which is driven by a nonlocal pressure. We consider constant parameters ...
• #### Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments ﻿

(SIAM Journal on Numerical Analysis, 2018)
\noindent We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations  \partial_t u-\mathfrak{L}[\varphi(u)]=f(x,t) \qquad\text{in}\qquad ...
• #### Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type ﻿

We study the uniqueness, existence, and properties of bounded distributional solutions of the initial value problem for the anomalous diffusion equation $\partial_tu-\mathcal{L}^\mu [\varphi (u)]=0$. Here $\mathcal{L}^\mu$ ...