Now showing items 1-6 of 6

• #### Discretizations of the spectral fractional Laplacian on general domains with Dirichlet, Neumann, and Robin boundary conditions ﻿

(2017-04-28)
In this work, we propose novel discretisations of the spectral fractional Laplacian on bounded domains based on the integral formulation of the operator via the heat-semigroup formalism. Specifically, we combine suitable ...
• #### 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 ...
• #### Modeling cardiac structural heterogeneity via space-fractional differential equations ﻿

(2017)
We discuss here the use of non-local models in space and fractional order operators in the characterisation of structural complexity and the modeling of propagation in heterogeneous biological tissues. In the specific, we ...
• #### 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 $\mathcal{L}^\mu$ ...