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Robust numerical methods for nonlocal (and local) equations of porous medium type. Part II: Schemes and experiments 

Del Teso, F.; Endal, J.; Jacobsen, E.R. (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 ...
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Asymptotic behaviour for fractional diffusion-convection equations 

Ignat, L.I.; Stan, D. (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 ...
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Existence of weak solutions for a general porous medium equation with nonlocal pressure 

Stan, D.; Del Teso, F.; Vázquez, J.L. (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 ...
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Uniqueness and Properties of Distributional Solutions of Nonlocal Equations of Porous Medium Type 

Del Teso, F.; Endal, J.; Jacobsen, E.R. (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 $\mathcal{L}^\mu$ ...

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AuthorDel Teso, F. (3)Endal, J. (2)Jacobsen, E.R. (2)Stan, D. (2)Ignat, L.I. (1)Vázquez, J.L. (1)Subject
fractional Laplacian (4)
convergence (2)distributional solutions (2)existence (2)nonlinear degenerate diffusion (2)nonlocal operators (2)porous medium equation (2)Stefan problem (2)uniqueness (2)a priori estimates (1)... másFecha2018 (1)2017 (2)2016 (1)

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