Timeline for Upper bound Hölder norm of the solution to the non-linear PDE $\partial_t u (t, x) = \Delta_x \{ |\sigma (u (t, x))|^2 u(t, x) \}$
Current License: CC BY-SA 4.0
18 events
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| Feb 21 at 21:16 | comment | added | Connor Mooney | If you let $H(s) := s\sigma^2(s)$ then the equation takes the appealing form $\partial_t(H(u)) = H'(u)\Delta(H(u))$. If $H' > 0$ then standard uniformly parabolic theory (e.g. from the book of Lieberman) can be applied. | |
| S Feb 14 at 11:07 | history | bounty ended | CommunityBot | ||
| S Feb 14 at 11:07 | history | notice removed | CommunityBot | ||
| Feb 13 at 10:04 | history | edited | Akira | CC BY-SA 4.0 |
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| Feb 13 at 10:04 | comment | added | Akira | @Fiktor Thank you for your comment! It is a typo and yess it should be $\sigma \in C_b^{1,\alpha}(\mathbb{R})$. By $\sigma^2(u(t,x))$, I meant $|\sigma(u(t,x))|^2$. | |
| Feb 11 at 20:54 | comment | added | Fiktor | Could you clarify? 1. Did you mean $\sigma \in C_b^{1,\alpha}(\mathbb{R})$? 2. By $\sigma^2(u(t,x))$, do you mean $\sigma(\sigma(u(t,x)))$ or $(\sigma(u(t,x)))^2$? | |
| Feb 10 at 18:46 | history | edited | Akira | CC BY-SA 4.0 |
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| S Feb 6 at 9:09 | history | bounty started | Akira | ||
| S Feb 6 at 9:09 | history | notice added | Akira | Authoritative reference needed | |
| Feb 3 at 15:01 | history | edited | Akira | CC BY-SA 4.0 |
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| Feb 3 at 11:56 | history | edited | Akira | CC BY-SA 4.0 |
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| Feb 3 at 11:49 | history | edited | Akira | CC BY-SA 4.0 |
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| S Jan 29 at 9:03 | history | bounty ended | CommunityBot | ||
| S Jan 29 at 9:03 | history | notice removed | CommunityBot | ||
| S Jan 21 at 6:39 | history | bounty started | Akira | ||
| S Jan 21 at 6:39 | history | notice added | Akira | Authoritative reference needed | |
| Jan 19 at 6:37 | history | edited | Akira | CC BY-SA 4.0 |
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| Jan 19 at 6:22 | history | asked | Akira | CC BY-SA 4.0 |