Publication

Cost for a controlled linear KdV equation

Joachim Krieger, Shengquan Xiang
2019
Journal Articles

Abstract

The controllability of the linearized KdV equation with right Neumann control is studied in the pioneering work of Rosier [25]. However, the proof is by contradiction arguments and the value of the observability constant remains unknown, though rich mathematical theories are built on this totally unknown constant. We introduce a constructive method that gives the quantitative value of this constant.

Official source

https://infoscience.epfl.ch/entities/publication/70e656b5-9776-44aa-94de-e9d20377ad28

About this result

This page is automatically generated and may contain information that is not correct, complete, up-to-date, or relevant to your search query. The same applies to every other page on this website. Please make sure to verify the information with EPFL's official sources.

Joachim Krieger, Shengquan Xiang
2019
Journal Articles

Abstract

Official source

https://infoscience.epfl.ch/entities/publication/70e656b5-9776-44aa-94de-e9d20377ad28

About this result

Related concepts (25)

Observable universe

The observable universe is a ball-shaped region of the universe comprising all matter that can be observed from Earth or its space-based telescopes and exploratory probes at the present time; the electromagnetic radiation from these objects has had time to reach the Solar System and Earth since the beginning of the cosmological expansion. Initially, it was estimated that there may be 2 trillion galaxies in the observable universe, although that number was reduced in 2021 to only several hundred billion based on data from New Horizons.

Contradiction

In traditional logic, a contradiction occurs when a proposition conflicts either with itself or established fact. It is often used as a tool to detect disingenuous beliefs and bias. Illustrating a general tendency in applied logic, Aristotle's law of noncontradiction states that "It is impossible that the same thing can at the same time both belong and not belong to the same object and in the same respect.

Proof by contradiction

In logic, proof by contradiction is a form of proof that establishes the truth or the validity of a proposition, by showing that assuming the proposition to be false leads to a contradiction. Although it is quite freely used in mathematical proofs, not every school of mathematical thought accepts this kind of nonconstructive proof as universally valid. More broadly, proof by contradiction is any form of argument that establishes a statement by arriving at a contradiction, even when the initial assumption is not the negation of the statement to be proved.

Related publications (31)

Euclid preparation XXXVI. Modelling the weak lensing angular power spectrum

Georges Meylan, Frédéric Courbin, Fabio Finelli, Richard Massey, Maurizio Martinelli, Gianluca Castignani, Marcello Farina, Austin Chandler Peel, Yi Wang

This work considers which higher order modeling e ffects on the cosmic shear angular power spectra must be taken into account for Euclid. We identified the relevant terms and quantified their individual and cumulative impact on the cosmological parameter i ...

Edp Sciences S A2024

Euclid: Validation of the MontePython forecasting tools

Slobodan Ilic, Georges Meylan, Frédéric Courbin, Julien Lesgourgues, Richard Massey, Maurizio Martinelli, Jean-Luc Starck, Yi Wang

Context. The Euclid mission of the European Space Agency will perform a survey of weak lensing cosmic shear and galaxy clustering in order to constrain cosmological models and fundamental physics. Aims. We expand and adjust the mock Euclid likelihoods of t ...

Edp Sciences S A2024

CURLING - I. The influence of point-like image approximation on the outcomes of cluster strong lens modelling

Nan Li, Jean-Paul Richard Kneib, Huanyuan Shan

Cluster-scale strong lensing is a powerful tool for exploring the properties of dark matter and constraining cosmological models. However, due to the complex parameter space, pixelized strong lens modelling in galaxy clusters is computationally expensive, ...

Oxford Univ Press2024