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

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

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

Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$

Joachim Krieger, Roland Donninger, Min Huang

For the critical focusing wave equation

\Box u = u^5

on

\mathbb{R}^{3+1}

in the radial case, we construct a family of blowup solutions which are obtained from the stationary solutions

W(r)

by means of a dynamical rescaling $\lambda(t)\frac{1}{2}W(\la ...

Michigan Mathematical Journal2014

Local discontinuous Galerkin methods for fractional diffusion equations

Jan Sickmann Hesthaven

We consider the development and analysis of local discontinuous Galerkin methods for fractional diffusion problems in one space dimension, characterized by having fractional derivatives, parameterized by beta in [1,2]. After demonstrating that a classic ap ...

EDP Sciences2013

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

Global dynamics away from the ground state for the energy-critical nonlinear wave equation

Joachim Krieger

We study global behavior of radial solutions for the nonlinear wave equation with the focusing energy critical nonlinearity in three and five space dimensions. Assuming that the solution has energy at most slightly more than the ground states and gets away ...

2013

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

Benchmarking Image-Processing Algorithms for Biomicroscopy: Reference Datasets and Perspectives

Michaël Unser, Daniel Sage, Cédric René Jean Vonesch, Hagay Kirshner, Stamatios Lefkimmiatis

As the field of bioimage informatics matures, the issue of the validation of image reconstruction algorithms and the definition of proper performance criteria becomes more pressing. In this work, we discuss benchmarking aspects of fluorescence microscopy q ...

EUSIPCO2013

Nonscattering solutions and blowup at infinity for the critical wave equation

Joachim Krieger, Roland Donninger

We consider the critical focusing wave equation (−∂2t+Δ)u+u5=0 in R1+3 and prove the existence of energy class solutions which are of the form u(t,x)=tμ2W(tμx)+η(t,x) in the forward lightcone {(t,x)∈R×R3:|x|≤t,t≫1} where W(x)=(1+13|x|2)−12 is the ground st ...

Springer Verlag2013

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

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

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

Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$

Local discontinuous Galerkin methods for fractional diffusion equations

Stochastic system controller synthesis for reachability specifications encoded by random sets

Global dynamics away from the ground state for the energy-critical nonlinear wave equation

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

Benchmarking Image-Processing Algorithms for Biomicroscopy: Reference Datasets and Perspectives

Nonscattering solutions and blowup at infinity for the critical wave equation

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

Stochastic system controller synthesis for reachability specifications encoded by random sets

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

Exotic blow up solutions for the $\Box u^5$-focussing wave equation in $\mathbb{R}^3$

Local discontinuous Galerkin methods for fractional diffusion equations

Nonscattering solutions and blowup at infinity for the critical wave equation

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

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

Partitioned Solution of Geometrical Multiscale Problems for the Cardiovascular System

Global dynamics away from the ground state for the energy-critical nonlinear wave equation

Benchmarking Image-Processing Algorithms for Biomicroscopy: Reference Datasets and Perspectives