Publications related to Local discontinuous Galerkin methods for fractional diffusion equations

Global Ill-Posedness of the Isentropic System of Gas Dynamics

Elisabetta Chiodaroli, Camillo De Lellis

We consider the isentropic compressible Euler system in 2 space dimensions with pressure law p () = (2) and we show the existence of classical Riemann data, i.e. pure jump discontinuities across a line, for which there are infinitely many admissible bounde ...

Wiley-Blackwell2015

A counterexample to well-posedness of entropy solutions to the compressible Euler system

Elisabetta Chiodaroli

We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the spatially periodic case. In more than one space dimension, the methods developed by De Lellis-Szekelyhidi enable us to show here failure of uniquenes ...

World Scientific Publ Co Pte Ltd2014

Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion

Ricardo Esteban Ruiz Baier

This paper is concerned with the study of pattern formation for an inhomogeneous Brusselator model with cross-diffusion, modeling an autocatalytic chemical reaction taking place in a three-dimensional domain. For the spatial discretization of the problem w ...

Elsevier2014

On the energy dissipation rate of solutions to the compressible isentropic Euler system

Elisabetta Chiodaroli

In this paper we extend and complement the results in [4] on the well-posedness issue for weak solutions of the compressible isentropic Euler system in 2 space dimensions with pressure law

p(\rho) = \rho^\gamme, \geq 1

. First we show that every Riemann p ...

Springer Verlag2014

Nondispersive solutions to the $L^2$-critical half-wave equation

Joachim Krieger

We consider the focusing

L^2

-critical half-wave equation in one space dimension

i \partial_t u = D u - |u|^2 u,

where

D

denotes the first-order fractional derivative. Standard arguments show that there is a critical threshold

M_* > 0

such that all ...

Springer Verlag2013

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

Alfio Quarteroni, Simone Deparis, Adelmo Cristiano Innocenza Malossi, Paolo Crosetto

Simulating arterial trees in the cardiovascular system can be made by the help of different models, depending on the outputs of interest and the desired degree of accuracy. In particular, one-dimensional fluid-structure interaction models for arteries are ...

Society for Industrial and Applied Mathematics2013

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Alfio Quarteroni, Christian Vergara, Luca Formaggia

In this work we discuss the reliability of the coupling among three-dimensional (3D) and one-dimensional (1D) models that describe blood flowing into the circulatory tree. In particular, we study the physical consistency of the 1D model with respect to the ...

Academic Press Inc Elsevier Science2013

Stochastic system controller synthesis for reachability specifications encoded by random sets

Maryam Kamgarpour, John Lygeros

We consider a reach–avoid specification for a stochastic hybrid dynamical system defined as reaching a goal set at some finite time, while avoiding an unsafe set at all previous times. In contrast with earlier works which consider the target and avoid sets ...

2013

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

Maria Colombo

We prove that solutions of a mildly regularized Perona–Malik equation converge, in a slow time scale, to solutions of the total variation flow. The convergence result is global-in-time, and holds true in any space dimension. The proof is based on the gener ...

2012

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Adelmo Cristiano Innocenza Malossi

The aim of this work is the development of a geometrical multiscale framework for the simulation of the human cardiovascular system under either physiological or pathological conditions. More precisely, we devise numerical algorithms for the partitioned so ...

EPFL2012

Local discontinuous Galerkin methods for fractional diffusion equations

Graph Chatbot

Chat with Graph Search

Global Ill-Posedness of the Isentropic System of Gas Dynamics

A counterexample to well-posedness of entropy solutions to the compressible Euler system

Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion

On the energy dissipation rate of solutions to the compressible isentropic Euler system

Nondispersive solutions to the $L^2$-critical half-wave equation

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Stochastic system controller synthesis for reachability specifications encoded by random sets

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

On the energy dissipation rate of solutions to the compressible isentropic Euler system

Nondispersive solutions to the $L^2$-critical half-wave equation

Stochastic system controller synthesis for reachability specifications encoded by random sets

Passing to the limit in maximal slope curves: from a regularized Perona–Malik equation to the total variation flow

A counterexample to well-posedness of entropy solutions to the compressible Euler system

Finite volume element approximation of an inhomogeneous Brusselator model with cross-diffusion

Implicit coupling of one-dimensional and three-dimensional blood flow models with compliant vessels

On the physical consistency between three-dimensional and one-dimensional models in haemodynamics

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Global Ill-Posedness of the Isentropic System of Gas Dynamics