Time translation symmetry: Difference between revisions

From DispersiveWiki
Jump to navigationJump to search
mNo edit summary
 
No edit summary
 
(One intermediate revision by one other user not shown)
Line 1: Line 1:
{{stub}}
{{stub}}


A PDE is said to have '''time translation symmetry''' if for any solution <math>u(t,x)</math> the function <math>u(t + t_0 , x)</math> is also a solution for all (or some interval of) <math>t_0 \in \mathbb{R}</math>.
A PDE is said to have '''time translation symmetry''' if for any solution <math>u(t,x)</math> the function <math>u(t + t_0 , x)</math> is also a solution for all (or some interval of) <math>t_0 \in \mathbb{R}</math>.  Generally speaking, a PDE has time translation symmetry when the coefficients and data do not explicitly involve the time variable t.


[[Categories:Stub]]
A PDE which has time-translation symmetry is also called ''time-translation invariant'' or ''autonomous''.
 
One can often use time-translation symmetry to bootstrap a local well-posedness result into a global well-posedness one, provided that one has some uniform control on the lifespan of the solution provided by the local well-posedness theory.

Latest revision as of 07:18, 20 December 2007


A PDE is said to have time translation symmetry if for any solution the function is also a solution for all (or some interval of) . Generally speaking, a PDE has time translation symmetry when the coefficients and data do not explicitly involve the time variable t.

A PDE which has time-translation symmetry is also called time-translation invariant or autonomous.

One can often use time-translation symmetry to bootstrap a local well-posedness result into a global well-posedness one, provided that one has some uniform control on the lifespan of the solution provided by the local well-posedness theory.