Parabolic perturbations of Hamilton–Jacobi equations

Yakov Sinai

Fundamenta Mathematicae (1998)

  • Volume: 157, Issue: 2-3, page 299-303
  • ISSN: 0016-2736

Abstract

top
We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.

How to cite

top

Sinai, Yakov. "Parabolic perturbations of Hamilton–Jacobi equations." Fundamenta Mathematicae 157.2-3 (1998): 299-303. <http://eudml.org/doc/212294>.

@article{Sinai1998,
abstract = {We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.},
author = {Sinai, Yakov},
journal = {Fundamenta Mathematicae},
keywords = {configuration space; phase space; invariant torus; family of tori; convergence},
language = {eng},
number = {2-3},
pages = {299-303},
title = {Parabolic perturbations of Hamilton–Jacobi equations},
url = {http://eudml.org/doc/212294},
volume = {157},
year = {1998},
}

TY - JOUR
AU - Sinai, Yakov
TI - Parabolic perturbations of Hamilton–Jacobi equations
JO - Fundamenta Mathematicae
PY - 1998
VL - 157
IS - 2-3
SP - 299
EP - 303
AB - We consider a parabolic perturbation of the Hamilton-Jacobi equation where the potential is periodic in space and time. We show that any solution converges to a limit not depending on initial conditions.
LA - eng
KW - configuration space; phase space; invariant torus; family of tori; convergence
UR - http://eudml.org/doc/212294
ER -

References

top
  1. [A] S. Aubry, The twist map, the extended Frenkel-Kontorova model and the devil's staircase, Phys. D 7 (1983), 240-258. Zbl0559.58013
  2. [JKM] H. R. Jauslin, H. O. Kreiss and J. Moser, On the forced Burgers equation with periodic boundary conditions, preprint, ETH, Zürich, 1997. Zbl0930.35156
  3. [M] J. Mather, Existence of quasi-periodic orbits for twist homeomorphisms of the annulus, Topology 21 (1982), 457-467. Zbl0506.58032
  4. [S] Ya. G. Sinai, Two results concerning asymptotic behavior of solutions of the Burgers equation with force, J. Statist. Phys. 64 (1991), 1-12. Zbl0978.35500

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.