5 papers
A Proximal Primal-Dual Approach to Generalized JKO Schemes for Doubly Nonlinear Parabolic Equations
Luis M. Briceño-Arias, José A. Carrillo, Dante Kalise +2
Variational methods based on optimization strategies are proposed to numerically solve a large family of nonlinear partial differential equations. They are all particular instances…
Well-posedness and mean-field limit of discontinuous weighted dynamics via the relative entropy method
Immanuel Ben Porat, José A. Carrillo, Alexandra Holzinger
We consider deterministic particle dynamics with time evolving weights and their associated Kolmogorov equation and mean-field equation. We prove existence and unique- ness for the…
Finite Element Approximation of the Fractional Porous Medium Equation
José A. Carrillo, Stefano Fronzoni, Endre Süli
We construct a finite element method for the numerical solution of a fractional porous medium equation on a bounded open Lipschitz polytopal domain , wher…
A frame approach for equations involving the fractional Laplacian
Ioannis P. A. Papadopoulos, Timon S. Gutleb, José A. Carrillo +1
Exceptionally elegant formulae exist for the fractional Laplacian operator applied to weighted classical orthogonal polynomials. We utilize these results to construct a solver, bas…
A minimax method for the spectral fractional Laplacian and related evolution problems
José A. Carrillo, Stefano Fronzoni, Yuji Nakatsukasa +1
We present a numerical method for the approximation of the inverse of the fractional Laplacian , based on its spectral definition, using rational functions to approximat…