Timeline for A comparison principle for parabolic equation
Current License: CC BY-SA 3.0
9 events
| when toggle format | what | by | license | comment | |
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| Jun 8, 2023 at 16:55 | comment | added | Fawen90 | @leomonsaingeon Further, how could you show that $\Delta a z \le 0$? | |
| Jun 7, 2023 at 13:02 | comment | added | Fawen90 | Dear Leo, as the linear maximum principle (applied to $z$) that you mentioned at the end, could you please provide a reference? Further, the $a$ appearing here is the function $a=a(x,t)$ or the constant $a=a(x_0,t_0)$? Many thanks for the clarification | |
| Apr 22, 2014 at 22:22 | comment | added | leo monsaingeon | No problem, you're very welcome! | |
| Apr 22, 2014 at 19:46 | vote | accept | riem | ||
| Apr 21, 2014 at 16:37 | comment | added | leo monsaingeon | One last comment: the "$a=\frac{F(u)-F(v)}{u-v}$" trick is preciesly what makes the duality method work for very weak solutions, see the proof of theorem 6.5 (with the extra difficulty that one first has to truncate to avoid the degenerate levelset $u=0$). | |
| Apr 21, 2014 at 16:31 | comment | added | leo monsaingeon | I updated my previous answer | |
| Apr 21, 2014 at 16:31 | history | edited | leo monsaingeon | CC BY-SA 3.0 |
added 865 characters in body
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| Apr 21, 2014 at 16:06 | comment | added | riem | Thank you Leo. I in fact was reading the very book. The author claims on page 95 the topic of my OP (near equation 5.27) but does not say why it is true. The theorem you cited I believe is more general (i.e. the weak formulation is different) so I believe whatever the comparison principle the author refers to on page 94 probably is simpler than the one on page 132 hence my question. | |
| Apr 21, 2014 at 15:46 | history | answered | leo monsaingeon | CC BY-SA 3.0 |