Outputs (20)

Convergence to equilibrium for a degenerate McKean-Vlasov Equation (2024)
Journal Article
Duong, M. H., & Einav, A. (2024). Convergence to equilibrium for a degenerate McKean-Vlasov Equation. Journal of Mathematical Physics, 65(12), https://doi.org/10.1063/5.0170283

In this work we study the convergence to equilibrium for a (po-tentially) degenerate nonlinear and nonlocal McKean-Vlasov equation. We show that the solution to this equation is related to the solution of a linear degenerate and/or defective Fokker-P... Read More about Convergence to equilibrium for a degenerate McKean-Vlasov Equation.

The Entropic journey of Kac's Model (2024)
Presentation / Conference Contribution
Einav, A. (2022, June). The Entropic journey of Kac's Model. Presented at PSPDE X: Particle Systems and Partial Differential Equations X, Braga, Portugal

The goal of this paper is to review the advances that were made during the last few decades in the study of the entropy, and in particular the entropy method, for Kac’s many particle system.

The Emergence of Order in Many Element Systems (2024)
Journal Article
Einav, A. (2024). The Emergence of Order in Many Element Systems. Journal of Statistical Physics, 191(7), Article 86. https://doi.org/10.1007/s10955-024-03307-7

Our work is dedicated to the introduction and investigation of a new asymptotic correlation relation in the field of mean field models and limits. This new notion, order (as opposed to chaos), revolves around a tendency for self organisation in a giv... Read More about The Emergence of Order in Many Element Systems.

Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems (2022)
Journal Article
Braukhoff, M., Einav, A., & Quoc Tang, B. (2022). Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems. Nonlinearity, 35(4), Article 1876. https://doi.org/10.1088/1361-6544/ac4d84

In this work we investigate the convergence to equilibriumfor mass action reactiondiffusion systemswhich model irreversible enzyme reactions. Using the standard entropy method in this situation is not feasible as the irreversibility of the system imp... Read More about Quantitative Dynamics of Irreversible Enzyme Reaction-Diffusion Systems.

Large Time Convergence of the Non-homogeneous Goldstein-Taylor Equation (2021)
Journal Article
Arnold, A., Einav, A., Signorello, B., & Wöhrer, T. (2021). Large Time Convergence of the Non-homogeneous Goldstein-Taylor Equation. Journal of Statistical Physics, 182(2), Article 41. https://doi.org/10.1007/s10955-021-02702-8

The Goldstein-Taylor equations can be thought of as a simplified version of a BGK system, where the velocity variable is constricted to a discrete set of values. It is intimately related to turbulent fluid motion and the telegrapher’s equation. A det... Read More about Large Time Convergence of the Non-homogeneous Goldstein-Taylor Equation.

Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems (2020)
Journal Article
Einav, A., Morgan, J. J., & Tang, B. Q. (2020). Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems. SIAM Journal on Mathematical Analysis, 52(5), 4314–4361. https://doi.org/10.1137/20m1319930

In this work we study global well-posedness and large time behavior for a typical reaction-diffusion system, which include degenerate diffusion, and whose nonlinearities arise from chemical reactions. We show that there is an indirect diffusion effec... Read More about Indirect Diffusion Effect in Degenerate Reaction-Diffusion Systems.

Weak Poincaré Inequalities in the Absence of Spectral Gaps (2019)
Journal Article
Ben-Artzi, J., & Einav, A. (2020). Weak Poincaré Inequalities in the Absence of Spectral Gaps. Annales Henri Poincaré, 21(2), 359–375. https://doi.org/10.1007/s00023-019-00858-4

For generators of Markov semigroups which lack a spectral gap, it is shown how bounds on the density of states near zero lead to a so-called weak Poincaré inequality (WPI), originally introduced by Liggett (Ann Probab 19(3):935–959, 1991). Applicatio... Read More about Weak Poincaré Inequalities in the Absence of Spectral Gaps.

Uniform moment propagation for the Becker--Döring equations (2018)
Journal Article
Cãnizo, J. A., Einav, A., & Lods, B. (2018). Uniform moment propagation for the Becker--Döring equations. Proceedings of the Royal Society of Edinburgh Section A: Mathematics, 149(4), 995-1015. https://doi.org/10.1017/prm.2018.99

We show uniform-in-time propagation of algebraic and stretched exponential moments for the Becker--Döring equations. Our proof is based upon a suitable use of the maximum principle together with known rates of convergence to equilibrium.

Interpolation of weighted Sobolev spaces (2018)
Journal Article
Cwikel, M., & Einav, A. (2019). Interpolation of weighted Sobolev spaces. Journal of Functional Analysis, 277(7), 2381-2441. https://doi.org/10.1016/j.jfa.2018.11.008

In this work we present a newly developed study of the interpolation of weighted Sobolev spaces by the complex method. We show that in some cases, one can obtain an analogue of the famous Stein–Weiss theorem for weighted Lp spaces. We consider an exa... Read More about Interpolation of weighted Sobolev spaces.

Entropy production inequalities for the Kac Walk (2018)
Journal Article
A. Carlen, E., C. Carvalho, M., & Einav, A. (2018). Entropy production inequalities for the Kac Walk. Kinetic and Related Models, 11(2), 219-238. https://doi.org/10.3934/krm.2018012

Mark Kac introduced what is now called 'the Kac Walk' with the aim of investigating the spatially homogeneous Boltzmann equation by probabilistic means. Much recent work, discussed below, on Kac's program has run in the other direction: using recent... Read More about Entropy production inequalities for the Kac Walk.