Timeline for Distance between solutions of differential inclusions
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| S Dec 7, 2023 at 1:08 | history | bounty ended | CommunityBot | ||
| S Dec 7, 2023 at 1:08 | history | notice removed | CommunityBot | ||
| S Nov 28, 2023 at 23:59 | history | bounty started | user479223 | ||
| S Nov 28, 2023 at 23:59 | history | notice added | user479223 | Draw attention | |
| Nov 24, 2023 at 12:52 | comment | added | Nate River | You probably also want a uniform in $t$ Lipschitz condition in $x$ for both $b_1$ and $b_2$, with respect to the above pointwise distance. | |
| Nov 24, 2023 at 12:48 | comment | added | Nate River | If we set up $b_1$ and $b_2$ so that the greedy choice is also globally optimal, we see that the bound given by the above is sharp. (2/2) | |
| Nov 24, 2023 at 12:47 | comment | added | Nate River | I feel like the appropriate distance between $b_1 (x, t)$ and $b_2 (x, t)$ should just be the simple $\sup_{a_1 \in b_1 (x, t), a_2 \in b_2(x, t)} |a_1 - a_2|$. And then you probably want $\text{dist}(b_1, b_2)$ to be the sup over $x, t$ of the above distance. The reason being that someone who wanted to ruin our day could just choose for $dY_1/dt$ and $dY_2/dt$ the worst possible choice (i.e. the one that maximises the difference). This is the locally optimal way to maximise the distance. (1/2) | |
| Nov 23, 2023 at 0:35 | history | edited | user479223 | CC BY-SA 4.0 |
added 22 characters in body
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| Nov 22, 2023 at 23:59 | history | asked | user479223 | CC BY-SA 4.0 |