Timeline for Uniqueness of weak solutions of a heat equation
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 10, 2014 at 19:23 | vote | accept | TW. | ||
| Sep 5, 2014 at 13:55 | comment | added | Joonas Ilmavirta | @TobiasWood, if $f$ does not depend on $t$, something similar to my approach might work, but I don't want to work it out. If $f$ depends on $t$, the Fourier transform gives a convolution term and things get a whole lot messier. My approach might be worth a try, but it doesn't look simple. | |
| Sep 5, 2014 at 10:55 | comment | added | TW. | Thank you for this answer. I have a question: suppose we replace the $-u$ with $f(x,t)u$ for some arbitrary space-time function $f$ (so the equation reads $u_t - \Delta u + fu=0$). I wonder then if I should integrate over and space and time and consider the operator $-\Delta u + f\text{Id}$ acting on $L^2(0,T;H^1)$ to $L^2(0,T;H^{-1})$. Maybe something similar to your answer would work. | |
| Sep 4, 2014 at 19:15 | history | answered | Joonas Ilmavirta | CC BY-SA 3.0 |