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Robust numerical methods for nonlocal (and local) equations of porous medium type. Part I: Theory
(2019)
Abstract. We develop a unified and easy to use framework to study robust fully discrete numerical methods for nonlinear degenerate diffusion equations
∂tu − Lσ,μ[φ(u)] = f(x,t) in RN × (0,T),
where Lσ,μ is a general ...
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 ...
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 $\mathcal{L}^\mu$ ...