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On extension problem, trace hardy and Hardy’s inequalities for some fractional Laplacians
(2019-09)
We obtain generalised trace Hardy inequalities for fractional powers of general operators given by sums of squares of vector fields. Such inequalities are derived by means of particular solutions of an extended equation ...
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 $\mathcal{L}^\mu$ ...