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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.
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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 ′ \mathcal {K}_e’ of distributions which "grow" no faster than exp ( e k | x |
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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
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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
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Bounds on short cylinders and uniqueness results for degenerate Kolmogorov equation [PDF]
, 2008 We consider the Cauchy problem for hypoelliptic Kolmogorov equations in both divergence and non divergence form. We prove that, if |u(x,t)| < M exp(a(t^{-\beta}+|x|^2)) for some positive constants a, M, \beta in ]0,1[ and u(x,0) = 0, then u(x,t) = 0 for ...
Cinti, Chiara, Polidoro, Sergio
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The Heat Equation with Singular Potentials. II: Hypoelliptic Case
Acta Applicandae Mathematicae, 2022 AbstractIn this paper we consider the heat equation with a strongly singular potential and show that it has a very weak solution. Our analysis is devoted to general hypoelliptic operators and is developed in the setting of graded Lie groups. The current work continues and extends the work (Altybay et al. in Appl. Math. Comput.
Marianna Chatzakou +2 more
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SLE and Virasoro representations: Fusion [PDF]
, 2014 We continue the study of null-vector equations in relation with partition functions of (systems of) Schramm-Loewner Evolutions (SLEs) by considering the question of fusion.
Dubédat, Julien
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Bounding stationary averages of polynomial diffusions via semidefinite programming [PDF]
, 2016 We introduce an algorithm based on semidefinite programming that yields increasing (resp. decreasing) sequences of lower (resp. upper) bounds on polynomial stationary averages of diffusions with polynomial drift vector and diffusion coefficients.
Barahona, Mauricio +3 more
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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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