Timeline for maximum principle for a non-uniformly parabolic operator
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
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| S Mar 20, 2014 at 13:35 | history | suggested | smyrlis | CC BY-SA 3.0 |
LaTeX improvement and typos.
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| Mar 20, 2014 at 13:33 | review | Suggested edits | |||
| S Mar 20, 2014 at 13:35 | |||||
| May 9, 2013 at 14:54 | answer | added | JCM | timeline score: 1 | |
| Apr 30, 2013 at 16:50 | comment | added | Luis Silvestre | What do you mean by the maximum principle? If you want the maximum of the solution to be decreasing in time, then it would not be true (even replacing the factor $e^{-\beta t}$ by $1$). If you want a comparison principle saying that if one solution is initially larger than another, then the order is preserved by time, then that will be true. If you want a bound on the $L^\infty$ norm for a solution $u$, then $||u(\cdot,t)||_{L^\infty} \leq e^{-(\min G_x)t} ||u(\cdot,0)||_{L^\infty}$ even if the second order term wasn't there. | |
| Apr 29, 2013 at 14:23 | comment | added | Thomas Richard | Since your equation is uniformly parabolic for $t\in [0,T]$ ($T$ bounded), most of the arguments should carry on... | |
| Apr 29, 2013 at 14:17 | history | asked | Mike | CC BY-SA 3.0 |