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Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments
(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 ...
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
(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 ...
Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type
(2016-09-01)
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 $\mathcal{L}^\mu$ ...