Timeline for How to solve this linear Cauchy Problem
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Sep 8, 2018 at 5:55 | comment | added | Andrew | The statements about uniqueness seems to be incorrect. As an example, make a change of variables (x,y): turn on $\pi/4$. The equation will have the same form. Put $a\equiv=-1$, $b\equiv c\equiv\ldots0$. Then the solution of the heat is not unique since no conditions on the segment's boundary are posed. | |
| Aug 9, 2018 at 6:33 | comment | added | utcyp | Hey, in order to show the existence and uniqueness I used Thm. 10 of Ch. 2.9 from Krylov in a $n$-dimensional space where I don't get these difficulties since I then have a open set (the $n$-dimensional probability simplex). Hence, the problem should be well-posted in more dimensions, isn't it? | |
| Aug 8, 2018 at 16:58 | comment | added | user35593 | Ok I didnt see that. But then how do you define the derivative by x and/or y if your function is only defined on the x+y=1 line? How did you prove existence and uniqueness? For me it seems the problem is not well-posed. | |
| Aug 8, 2018 at 8:58 | comment | added | utcyp | Hey user35593, thanks for your reply. I only have these constraints. Actually, my domain should be a line segment. Therefore, I guess that it is not possible to discretize it. | |
| Aug 7, 2018 at 17:23 | comment | added | user35593 | do you have some additional constraints on the boundary of your triangle? You could use a uniform grid and do some finite differences. | |
| Aug 7, 2018 at 16:10 | review | First posts | |||
| Aug 7, 2018 at 16:34 | |||||
| Aug 7, 2018 at 16:09 | history | asked | utcyp | CC BY-SA 4.0 |