Talk:Well-posed problem: Difference between revisions
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imported>Paul Wormer No edit summary |
imported>Peter Schmitt (ill-conditioned) |
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I don't know anything about chaos, but I'm told that non-linear partial differential equations can have "chaotic" solutions. A very small change in initial conditions can give very large effects later (the famous flapping of a butterfly wing in Brazil causing a hurricane in Texas). Are problems with chaotic solutions well-posed?--[[User:Paul Wormer|Paul Wormer]] 13:47, 19 March 2010 (UTC) | I don't know anything about chaos, but I'm told that non-linear partial differential equations can have "chaotic" solutions. A very small change in initial conditions can give very large effects later (the famous flapping of a butterfly wing in Brazil causing a hurricane in Texas). Are problems with chaotic solutions well-posed?--[[User:Paul Wormer|Paul Wormer]] 13:47, 19 March 2010 (UTC) | ||
: These chaotic systems are deterministic and also continuous, but ill-conditioned (not stable). Therefore well-posed. It seems that a few authors include stable into well-posed, but most do not and the canonical definition seems to demand continuity only. --[[User:Peter Schmitt|Peter Schmitt]] 23:51, 20 March 2010 (UTC) | |||
Latest revision as of 17:51, 20 March 2010
I don't know anything about chaos, but I'm told that non-linear partial differential equations can have "chaotic" solutions. A very small change in initial conditions can give very large effects later (the famous flapping of a butterfly wing in Brazil causing a hurricane in Texas). Are problems with chaotic solutions well-posed?--Paul Wormer 13:47, 19 March 2010 (UTC)
- These chaotic systems are deterministic and also continuous, but ill-conditioned (not stable). Therefore well-posed. It seems that a few authors include stable into well-posed, but most do not and the canonical definition seems to demand continuity only. --Peter Schmitt 23:51, 20 March 2010 (UTC)