Zobrazeno 1 - 10 of 15 pro vyhledávání: '"Alexandre Boritchev"'
2
Sharp Sobolev Estimates for Concentration of Solutions to an Aggregation–Diffusion Equation
Autor: Grzegorz Karch, Alexandre Boritchev, Philippe Laurençot, Piotr Biler
Publikováno v: Journal of Dynamics and Differential Equations
Journal of Dynamics and Differential Equations, 2022, 34, pp.3131--3141. ⟨10.1007/s10884-021-09998-w⟩
We consider the drift-diffusion equation $$\begin{aligned} u_t-\varepsilon \varDelta u+\nabla \cdot (u\ \nabla K*u)=0 \end{aligned}$$ in the whole space with global-in-time solutions bounded in all Sobolev spaces; for simplicity, we restrict ourselve
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f9ca171a6c80ee15d5dfee04cb900a2c
https://doi.org/10.1007/s10884-021-09998-w
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4
Concentration phenomena in a diffusive aggregation model
Autor: Philippe Laurençot, Grzegorz Karch, Piotr Biler, Alexandre Boritchev
Publikováno v: Journal of Differential Equations
Journal of Differential Equations, Elsevier, 2021, 271, pp.1092--1108
Journal of Differential Equations, 2021, 271, pp.1092--1108. ⟨10.1016/j.jde.2020.09.035⟩
We consider the drift-diffusion equation u t − e Δ u + ∇ ⋅ ( u ∇ K ⁎ u ) = 0 in the whole space with global-in-time bounded solutions. Mass concentration phenomena for radially symmetric solutions of this equation with small diffusivity ar
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::da22cdf987f457078eebcb6bf3b3e008
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5
Exponential convergence to the stationary measure for a class of 1D Lagrangian systems with random forcing
Autor: Alexandre Boritchev
Publikováno v: Stochastics and Partial Differential Equations: Analysis and Computations
Stochastics and Partial Differential Equations: Analysis and Computations, Springer US, 2018, 6 (1), pp.109-123. ⟨10.1007/s40072-017-0104-7⟩
We prove exponential convergence to the stationary measure for a class of 1d Lagrangian systems with random forcing in the space-periodic setting: $$\begin{aligned} \phi _t+\phi _x^2/2=F^{\omega },\ x \in S^1=\mathbb {R}/\mathbb {Z}. \end{aligned}$$
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::97ebcc13855b56dfd342edf639fdcb48
https://doi.org/10.1007/s40072-017-0104-7
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6
Intermittency of Riemann's non-differentiable function through the fourth-order flatness
Autor: Daniel Eceizabarrena, Victor Vilaça da Rocha, Alexandre Boritchev
Publikováno v: Journal of Mathematical Physics
Journal of Mathematical Physics, 2021, 62 (9), pp.093101. ⟨10.1063/5.0011569⟩
Riemann's non-differentiable function is one of the most famous examples of continuous but nowhere differentiable functions, but it has also been shown to be relevant from a physical point of view. Indeed, it satisfies the Frisch-Parisi multifractal
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1b05fb4648e5602933591908d62de2ec
http://arxiv.org/abs/1910.13191
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7
Decaying Turbulence in the Generalised Burgers Equation
Autor: Alexandre Boritchev
Publikováno v: Archive for Rational Mechanics and Analysis
We consider the generalised Burgers equation $$\frac{\partial u}{\partial t} + f'(u)\frac{\partial u}{\partial x} - \nu \frac{\partial^2 u}{\partial x^2} = 0, \,\, t \geqq 0, \,\, x \in S^1,$$ ∂ u ∂ t + f ′ ( u ) ∂ u ∂ x - ν ∂ 2 u ∂ x
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::479816f0266ac89345ff26be6ce0cdcf
http://doc.rero.ch/record/325658/files/205_2014_Article_766.pdf
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8
Decaying turbulence for the fractional subcritical Burgers equation
Autor: Alexandre Boritchev
Publikováno v: Discrete & Continuous Dynamical Systems-A
Discrete & Continuous Dynamical Systems-A, 2018, 38 (5), pp.2229-2249. ⟨10.3934/dcds.2018092⟩
We consider the fractional unforced Burgers equation in the one-dimensional space-periodic setting: $$\partial u/\partial t+(f(u))_x +\nu \Lambda^{\alpha} u= 0, t \geq 0,\ \mathbb{x} \in \mathbb{T}^d=(\mathbb{R}/\mathbb{Z})^d.$$ Here $f$ is strongly
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::cb112b697d8bebfbd1721b763d559604
https://hal.archives-ouvertes.fr/hal-02069968
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9
Estimates for solutions of a low-viscosity kick-forced generalized Burgers equation
Autor: Alexandre Boritchev
Publikováno v: Proceedings of the Royal Society of Edinburgh: Section A Mathematics. 143:253-268
We consider a non-homogeneous generalized Burgers equationHere, ν is small and positive, f is strongly convex and satisfies a growth assumption, while ηω is a space-smooth random ‘kicked’ forcing term. For any solution u of this equation, we c
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_________::26ffdc7c6b28baa2f4c3b554d41c8b74
https://doi.org/10.1017/s0308210511000989
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10
Multidimensional Potential Burgers Turbulence
Autor: Alexandre Boritchev
Publikováno v: Communications in Mathematical Physics
Communications in Mathematical Physics, Springer Verlag, 2016, 342 (1), pp.441-489. ⟨10.1007/s00220-015-2521-7⟩
Communications in Mathematical Physics, 2016, 342 (1), pp.441-489. ⟨10.1007/s00220-015-2521-7⟩
We consider the multidimensional generalised stochastic Burgers equation in the space-periodic setting: $ \partial \mathbf{u}/\partial t+$ $(\nabla f(\mathbf{u}) \cdot \nabla)$ $\mathbf{u} -\nu \Delta \mathbf{u}=$ $\nabla \eta,\quad t \geq 0,\ \mathb
Externí odkaz: https://explore.openaire.eu/search/publication?articleId=doi_dedup___::1329ecb1462733468a4d054e4bbee035
https://hal.archives-ouvertes.fr/hal-01468550
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