Results 21 to 30 of about 125 (115)

FRACTIONAL ORDER KINETIC EQUATIONS AND HYPOELLIPTICITY [PDF]

Analysis and Applications, 2012
We give simple proofs of hypoelliptic estimates for some models of kinetic equations with a fractional order diffusion part. The proofs are based on energy estimates together with the previous ideas of Bouchut and Perthame.
openaire   +3 more sources

Hypoelliptic convolution equations in the space 𝒦’ₑ [PDF]

Transactions of the American Mathematical Society, 1986
We consider convolution equations in the space K e ′
openaire   +1 more source

Hypoellipticity and the Mori–Zwanzig formulation of stochastic differential equations [PDF]

Journal of Mathematical Physics, 2021
We develop a thorough mathematical analysis of the effective Mori–Zwanzig (EMZ) equation governing the dynamics of noise-averaged observables in stochastic differential equations driven by multiplicative Gaussian white noise. Building upon recent work on hypoelliptic operators, we prove that the EMZ memory kernel and fluctuation terms converge ...
Yuanran Zhu, Daniele Venturi
openaire   +5 more sources

Hypoellipticity for a class of kinetic equations

Kyoto Journal of Mathematics, 2007
The authors consider the following linearized version of Boltzmann equation without angular cutoff: \[ Pu= \partial_t+ x\nabla_y u+ \sigma(-\widetilde\Delta_x)^\lambda u= f, \] where \((x,y)\in \mathbb{R}^{2n}\) and \(\sigma> 0\). Here \((-\widetilde\Delta_x)^\lambda\) is a Fourier multiplier with symbol \(|\eta|^{2\lambda}\) if \(|\eta|\geq 2\), and \(
Xu, Chao-Jiang, Morimoto, Yoshinori
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Theory of B(X)‐Module: Algebraic Module Structure of Generally Unbounded Infinitesimal Generators

Advances in Mathematical Physics, Volume 2020, Issue 1, 2020., 2020
The concept of logarithmic representation of infinitesimal generators is introduced, and it is applied to clarify the algebraic structure of bounded and unbounded infinitesimal generators. In particular, by means of the logarithmic representation, the bounded components can be extracted from generally unbounded infinitesimal generators.
Yoritaka Iwata, Ricardo Weder
wiley   +1 more source

Hypoelliptic regularity in kinetic equations

Journal de Mathématiques Pures et Appliquées, 2002
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Remarks on hypoelliptic equations

Annales Henri Lebesgue
Many results of smooth hypoellipticity are available for scalar equations. Much remains to be done for systems and/or at different levels of regularity and in particular for L 1
Banica, Valeria, Burq, Nicolas
openaire   +2 more sources

The Gevrey hypoellipticity for kinetic equations

, 2011
In this paper, we study the Gevrey regularity of weak solutions for a class of linear and semi-linear kinetic equations, which are the linear model of spatially inhomogeneous Boltzmann equations without an angular cutoff.
Chen, Hua, Li, Weixi, Xu, Chao-Jiang
openaire   +2 more sources

On the completeness of the space OC$\mathcal {O}_C$

Mathematische Nachrichten, Volume 298, Issue 8, Page 2740-2748, August 2025.
Abstract We explicitly prove the compact regularity of the LF$\mathcal {LF}$‐space of double sequences limk→(s⊗̂(ℓp)k)≅limk→(s⊗̂(c0)−k)$ {\lim _{k\rightarrow }} (s\widehat{\otimes }(\ell ^p)_{k}) \cong {\lim _{k\rightarrow }}(s\widehat{\otimes }(c_0)_{-k})$, 1≤p≤∞$1\le p\le \infty$.
Michael Kunzinger, Norbert Ortner
wiley   +1 more source

A Theory of Generalized Coordinates for Stochastic Differential Equations

Studies in Applied Mathematics, Volume 154, Issue 5, May 2025.
ABSTRACT Stochastic differential equations are ubiquitous modeling tools in applied mathematics and the sciences. In most modeling scenarios, random fluctuations driving dynamics or motion have some nontrivial temporal correlation structure, which renders the SDE non‐Markovian; a phenomenon commonly known as ‘colored’’ noise.
Lancelot Da Costa, Nathaël Da Costa, Conor Heins, Johan Medrano, Grigorios A. Pavliotis, Thomas Parr, Ajith Anil Meera, Karl Friston   +7 more
wiley   +1 more source