Publications related to On the equation A del u plus (del u)(t) A = G

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

In this thesis, we study two distinct problems. The first problem consists of studying the linear system of partial differential equations which consists of taking a k-form, and applying the exterior derivative 'd' to it and add the wedge product with a 1- ...

EPFL2018

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Jean-Philippe Lucien Montillet

Families of energy operators and generalized energy operators have recently been introduced in the definition of the solutions of linear Partial Differential Equations (PDEs) with a particular application to the wave equation [ 15]. To do so, the author ha ...

Int Center Scientific Research & Studies2017

Detecting Anisotropic Inclusions Through EIT

Jan Cristina

We study the evolution equation where is the Dirichlet-Neumann operator of a decreasing family of Riemannian manifolds with boundary . We derive a lower bound for the solution of such an equation, and apply it to a quantitative density estimate for the res ...

Springer2017

Stochastic partial differential equations driven by Lévy white noises

Thomas Marie Jean-Baptiste Humeau

We study various aspects of stochastic partial differential equations driven by Lévy white noise. This driving noise, which is a generalization of Gaussian white noise, can be viewed either as a generalized random process or as an independently scattered r ...

EPFL2017

A Class Of Large Global Solutions For The Wave-Map Equation

Joachim Krieger, Elisabetta Chiodaroli

In this paper we consider the equation for equivariant wave maps from R3+1 to S-3 and we prove global in forward time existence of certain C-infinity-smooth solutions which have infinite critical Sobolev norm (H) overdot(3/4) (R-3) x (H) overdot(1/2) (R-3) ...

2017

Dynamical Low Rank approximation of PDEs with random parameters

Eleonora Musharbash

In this work, we focus on the Dynamical Low Rank (DLR) approximation of PDEs equations with random parameters. This can be interpreted as a reduced basis method, where the approximate solution is expanded in separable form over a set of few deterministic b ...

EPFL2017

Renormalized solutions to the continuity equation with an integrable damping term

Maria Colombo

We consider the continuity equation with a nonsmooth vector field and a damping term. In their fundamental paper, DiPerna and Lions (Invent Math 98:511-547, 1989) proved that, when the damping term is bounded in space and time, the equation is well posed i ...

2015

Optimal transport of closed differential forms for convex costs

Bernard Dacorogna, Olivier Kneuss

Let c : A(k-1) -> R+ be convex and Omega subset of R-n be a bounded domain. Let f(0) and f(1) be two closed k-forms on Omega satisfying appropriate boundary conditions. We discuss the minimization of integral(Omega) c (A) dx over a subset of (k - 1)-forms ...

Elsevier France-Editions Scientifiques Medicales Elsevier2015

Some New Results On Differential Inclusions For Differential Forms

Bernard Dacorogna, Olivier Kneuss, Saugata Bandyopadhyay

In this article we study some necessary and sufficient conditions for the existence of solutions in W-0(1,infinity) (Omega; Lambda(k)) of the differential inclusion d omega is an element of E a.e. in Omega where E subset of Lambda(k+1) is a prescribed set. ...

Amer Mathematical Soc2015

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$

Joachim Krieger

For the radial energy-supercritical nonlinear wave equation

\Box u = -u_{tt} + \triangle u = \pm u^7

on

\R^{3+1}

, we prove the existence of a class of global in forward time

C^\infty

-smooth solutions with infinite critical Sobolev norm $\dot{H}^{\f ...

Springer Verlag2014

On the equation A del u plus (del u)(t) A = G

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Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Detecting Anisotropic Inclusions Through EIT

Stochastic partial differential equations driven by Lévy white noises

A Class Of Large Global Solutions For The Wave-Map Equation

Dynamical Low Rank approximation of PDEs with random parameters

Renormalized solutions to the continuity equation with an integrable damping term

Optimal transport of closed differential forms for convex costs

Some New Results On Differential Inclusions For Differential Forms

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$

Optimal transport of closed differential forms for convex costs

Some New Results On Differential Inclusions For Differential Forms

Renormalized solutions to the continuity equation with an integrable damping term

Sur quelques équations aux dérivées partielles en lien avec le lemme de Poincaré

Dynamical Low Rank approximation of PDEs with random parameters

Detecting Anisotropic Inclusions Through EIT

Multiplicity Of Solutions For Linear Partial Differential Equations Using (Generalized) Energy Operators

Stochastic partial differential equations driven by Lévy white noises

A Class Of Large Global Solutions For The Wave-Map Equation

Large global solutions for energy supercritical nonlinear wave equations on $\R^{3+1}$