Publications related to Fredholm transformation on Laplacian and rapid stabilization for the heat equations

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

We present outlier-free isogeometric Galerkin discretizations of eigenvalue problems related to the biharmonic and the polyharmonic operator in the univariate setting. These are Galerkin discretizations in certain spline subspaces that provide accurate app ...

Lausanne2023

Fredholm transformation on Laplacian and rapid stabilization for the heat equation

Shengquan Xiang

We study the rapid stabilization of the heat equation on the 1-dimensional torus using the backstepping method with a Fredholm transformation. This classical framework allows us to present the backstepping method with Fredholm transformations for the Lapla ...

ACADEMIC PRESS INC ELSEVIER SCIENCE2022

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Raphaël Jean Berthier

Gossip algorithms and their accelerated versions have been studied exclusively in discrete time on graphs. In this work, we take a different approach and consider the scaling limit of gossip algorithms in both large graphs and large number of iterations. T ...

OXFORD UNIV PRESS2022

A dependence of the cost of fast controls for the heat equation on the support of initial datum

Hoài-Minh Nguyên

The controllability cost for the heat equation as the control time

T

goes to 0 is well-known of the order

e^{C/T}

for some positive constant

C

, depending on the controlled domain and for all initial datum. In this paper, we prove that the constant $C ...

2021

Reference tracking stochastic model predictive control over unreliable channels and bounded control actions

Colin Neil Jones

A stochastic model predictive control framework over unreliable Bernoulli communication channels, in the presence of unbounded process noise and under bounded control inputs, is presented for tracking a reference signal. The data losses in the control chan ...

2021

Quantitative rapid and finite time stabilization of the heat equation

Shengquan Xiang

The null controllability of the heat equation is known for decades [21, 25, 34]. The finite time stabilizability of the one dimensional heat equation was proved by Coron-Nguyên [15], while the same question for high dimensional spaces remained widely open. ...

2020

Generalization of Fourier’s Law into Viscous Heat Equations

Nicola Marzari, Andrea Cepellotti, Michele Simoncelli

Heat conduction in dielectric crystals originates from the dynamics of atomic vibrations, whose evolution is well described by the linearized Boltzmann transport equation for the phonon populations. Recently, it was shown that thermal conductivity can be r ...

2020

Kernel methods and Model predictive approaches for Learning and Control

Sanket Sanjay Diwale

Data-driven modeling and feedback control play a vital role in several application areas ranging from robotics, control theory, manufacturing to management of assets, financial portfolios and supply chains. Many such problems in one way or another are rela ...

EPFL2019

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Robert Dalang, Thomas Marie Jean-Baptiste Humeau

We study the notions of mild solution and generalized solution to a linear stochastic partial differential equation driven by a pure jump symmetric Levy white noise, with symmetric alpha-stable Levy white noise as an important special case. We identify con ...

UNIV WASHINGTON, DEPT MATHEMATICS2019

Local Well-Posedness And Blow-Up For The Half Ginzburg-Landau-Kuramoto Equation With Rough Coefficients And Potential

Luigi Forcella

We study the Cauchy problem for the half Ginzburg- Landau-Kuramoto (hGLK) equation with the second order elliptic operator having rough coecients and potential type perturbation. The blow-up of solutions for hGLK equation with non-positive nonlinearity is ...

2019

Fredholm transformation on Laplacian and rapid stabilization for the heat equations

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Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

Fredholm transformation on Laplacian and rapid stabilization for the heat equation

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

A dependence of the cost of fast controls for the heat equation on the support of initial datum

Reference tracking stochastic model predictive control over unreliable channels and bounded control actions

Quantitative rapid and finite time stabilization of the heat equation

Generalization of Fourier’s Law into Viscous Heat Equations

Kernel methods and Model predictive approaches for Learning and Control

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Local Well-Posedness And Blow-Up For The Half Ginzburg-Landau-Kuramoto Equation With Rough Coefficients And Potential

Reference tracking stochastic model predictive control over unreliable channels and bounded control actions

Outlier-free spline spaces for isogeometric discretizations of biharmonic and polyharmonic eigenvalue problems

Kernel methods and Model predictive approaches for Learning and Control

Acceleration of gossip algorithms through the Euler-Poisson-Darboux Equation

Fredholm transformation on Laplacian and rapid stabilization for the heat equation

Quantitative rapid and finite time stabilization of the heat equation

Generalization of Fourier’s Law into Viscous Heat Equations

Random field solutions to linear SPDEs driven by symmetric pure jump Levy space-time white noises

Local Well-Posedness And Blow-Up For The Half Ginzburg-Landau-Kuramoto Equation With Rough Coefficients And Potential

A dependence of the cost of fast controls for the heat equation on the support of initial datum