[過去ﾛｸﾞ] 現代数学の系譜11 ガロア理論を読む27 [無断転載禁止]©2ch.net (517ﾚｽ)
上下前次1-新

---

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索 歴削→次ｽﾚ 栞削→次ｽﾚ 過去ﾛｸﾞﾒﾆｭｰ

---

262: 現代数学の系譜11 ガロア理論を読む 2017/01/02(月)13:15 ID:MUXssChK(42/59) AAS
>>242 関連

外部ﾘﾝｸ:en.wikipedia.org
(抜粋)
In physics, Landau damping, named after its discoverer,[1] the eminent Soviet physicist Lev Landau (1908?68), is the effect of damping (exponential decrease as a function of time) of longitudinal space charge waves in plasma or a similar environment.[2]
This phenomenon prevents an instability from developing, and creates a region of stability in the parameter space.

Landau damping can be manipulated exactly in numerical simulations such as particle-in-cell simulation.[5] It was proved to exist experimentally by Malmberg and Wharton in 1964,[6] almost two decades after its prediction by Landau in 1946.[7]

Mathematical theory: the Cauchy problem for perturbative solutions

The rigorous mathematical theory is based on solving the Cauchy problem for the evolution equation (here the partial differential Vlasov?Poisson equation) and proving estimates on the solution.

First a rather complete linearized mathematical theory has been developed since Landau.[14]

In a recent paper[17] the initial data issue is solved and Landau damping is mathematically established for the first time for the non-linear Vlasov equation.
It is proved that solutions starting in some neighborhood (for the analytic or Gevrey topology) of a linearly stable homogeneous stationary solution are (orbitally) stable for all times and are damped globally in time.
The damping phenomenon is reinterpreted in terms of transfer of regularity of f {\displaystyle f} f as a function of x {\displaystyle x} x and v {\displaystyle v} v, respectively, rather than exchanges of energy.

17 Mouhot, C., and Villani, C. "On Landau damping", Acta Math. 207, 1 (2011), 29?201 (quoted for the Fields Medal awarded to Cedric Villani in 2010)

---

上下前次1-新書関写板覧索設栞歴

---

あと 255 ﾚｽあります
ｽﾚ情報 赤ﾚｽ抽出 画像ﾚｽ抽出 歴の未読ｽﾚ AAｻﾑﾈｲﾙ

---

ぬこの手 ぬこTOP 0.007s