Timeline for Exercise 5.9. of the book A Basic Course in Partial Differential Equations, by Qing Han, about application of strong maximum principle
Current License: CC BY-SA 4.0
6 events
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| May 18, 2020 at 21:45 | comment | added | leo monsaingeon | I'll leave you figure out the construction of the supersolution $\overline u(t)$ by solving some other ODE, which is going to be slightly more involved due to the $e^{-u}$ to be taken into account (this nonnegative term was simply discarded in the construction of the subsolution). | |
| May 18, 2020 at 21:43 | comment | added | leo monsaingeon | It is much simpler than that: construct a suitable constant-in space subsolution $\underline u(t,x)=\underline u(t)$ by solving the (trivial) ODE $\frac{d}{dt}\underline u=-\|f\|_\infty$ starting from $\underline u(0):=-\max\{\|u_0\|_\infty,\|\phi\|_\infty\}$, which can be explicited as $\underline u(t)=-T \|f\|-\max\{\|u_0\|_\infty,\|\phi\|_\infty\}$ The maximum principle then gives $u(t,x)\geq \underline u(t)$ in the whole domain (the parabolic boundary conditions are automatically ordered). | |
| S May 20, 2019 at 10:30 | history | suggested | user64494 | CC BY-SA 4.0 |
A typo in the title is corrected.
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| May 20, 2019 at 10:03 | review | Suggested edits | |||
| S May 20, 2019 at 10:30 | |||||
| May 20, 2019 at 8:15 | history | edited | Hheepp | CC BY-SA 4.0 |
added 5 characters in body
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| May 20, 2019 at 7:46 | history | asked | Hheepp | CC BY-SA 4.0 |