Publications related to Nonlinear Stability of Self-Similar Solutions for Semilinear Wave Equations

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

The objective of this dissertation is to develop data-driven frequency-domain methods for designing robust controllers through the use of convex optimization algorithms. Many of today's industrial processes are becoming more complex, and modeling accurate ...

EPFL2018

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

Timothée Noé Pouchon, Assyr Abdulle

A family of effective equations for the wave equation in locally periodic media over long time is derived. In particular, explicit formulas for the effective tensors are provided. To validate the derivation, an a priori error estimate between the effective ...

MATHICSE2017

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash, Eva Vidlicková

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of 2S dynamical ...

MATHICSE2017

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

Fabio Nobile, Eleonora Musharbash

In this paper we propose a dynamical low-rank strategy for the approximation of second order wave equations with random parameters. The governing equation is rewritten in Hamiltonian form and the approximate solution is expanded over a set of

2S

dynamica ...

2017

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

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Joachim Krieger, Roland Donninger

We study the Cauchy problem for the one-dimensional wave equation

\partial_t^2 u(t,x)-\partial_x^2 u(t,x)+V(x)u(t,x)=0.

The potential

V

is assumed to be smooth with asymptotic behavior

V(x)\sim -\tfrac14 |x|^{-2}\mbox{ as } |x|\to \infty.

...

2016

Stable self-similar blowup in energy supercritical Yang-Mills theory

Roland Donninger

We consider the Cauchy problem for an energy supercritical nonlinear wave equation that arises in -dimensional Yang-Mills theory. A certain self-similar solution of this model is conjectured to act as an attractor for generic large data evolutions. Assumin ...

Springer Verlag2014

On the stability of travelling waves with vorticity obtained by minimization

Boris Buffoni

We modify the approach of Burton and Toland Comm. Pure Appl. Math. LXIV. 975-1007 (2011) to show the existence of periodic surface water waves with vorticity in order that it becomes suited to a stability analysis. This is achieved by enlarging the functio ...

Springer Basel2013

Revisiting the Limit Behaviour of ``El Botellon"

Jean-Yves Le Boudec

Emergent phenomena occur due to the pattern of non-linear and distributed local interactions between the elements of a system over time. An example of such phenomena is the spontaneous self-organisation of drinking parties in the squares of cities in Spain ...

2012

On stable self-similar blow up for equivariant wave maps: The linearized problem

Roland Donninger

We consider co-rotational wave maps from (3+1) Minkowski space into the three-sphere. This is an energy supercritical model which is known to exhibit finite time blow up via self-similar solutions. The ground state self-similar solution

f_0

is known in c ...

2012

Nonlinear Stability of Self-Similar Solutions for Semilinear Wave Equations

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A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

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

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Stable self-similar blowup in energy supercritical Yang-Mills theory

On the stability of travelling waves with vorticity obtained by minimization

Revisiting the Limit Behaviour of ``El Botellon"

On stable self-similar blow up for equivariant wave maps: The linearized problem

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

A Data-Driven Frequency-Domain Approach for Robust Controller Design via Convex Optimization

On the stability of travelling waves with vorticity obtained by minimization

MATHICSE Technical Report : Symplectic dynamical low rank approximation of wave equations with random parameters

Stable self-similar blowup in energy supercritical Yang-Mills theory

MATHICSE Technical Report : Effective models for long time wave propagation in locally periodic media

Symplectic Dynamical Low Rank approximation of wave equations with random parameters

A vector field method on the distorted Fourier side and decay for wave equations with potentials

Revisiting the Limit Behaviour of ``El Botellon"

On stable self-similar blow up for equivariant wave maps: The linearized problem