Timeline for Regularity of the mild solution of a semilinear evolution equation
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| Feb 7, 2020 at 1:27 | history | edited | YCor | CC BY-SA 4.0 |
fixed typo
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| Jan 6, 2017 at 22:30 | comment | added | 0xbadf00d | (b) What can we say about $\frac{{\rm d}u}{{\rm d}t}$? The book states $\frac{{\rm d}u}{{\rm d}t}∈\mathcal D(A^{-1/2})$ which doesn't make much sense, since $\mathcal D(A^β)=H$ for all $β≤0$; if I'm not terribly wrong. Moreover, the book states that $\frac{{\rm d}u}{{\rm d}t}$ satisfies $(16)$ (from the comments below the question), which should imply $\frac{{\rm d}u}{{\rm d}t}\in H$. And I'm curious whether $(19)$ can be concluded from $(18)$, since I see no other way to obtain $(16)$. | |
| Jan 6, 2017 at 22:30 | comment | added | 0xbadf00d | There are two questions: (a) I claim that $u(t)\in\mathcal D(A^α)$ for all $α<1$ by the same argument as in the book. Can we show more? | |
| Jan 6, 2017 at 20:41 | history | answered | Kira G. | CC BY-SA 3.0 |