Timeline for Existence for ODE in Banach space (accretive operators and Crandall-Liggett)
Current License: CC BY-SA 3.0
4 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 14, 2014 at 8:55 | vote | accept | TheBook | ||
| Apr 2, 2014 at 14:49 | comment | added | TheBook | ..My understanding is, if the right hand side $F(u) = -A(u) + f$ is nice enough, then it ought to. Does that make sense? Maybe this is what you meant by structural properties. I mean I don't see anything special about the time derivative... | |
| Apr 2, 2014 at 14:49 | comment | added | TheBook | Thanks for the answer. I see now that a mild solution is defined as the limit of the discretised solutions as you said. My intention is to obtain such a mild solution and then use some properties of my particular problem to show that it is a weak/strong solution too. If I have the equation $F(u) + A(u) = f$ as in the OP, let me write instead $u_n - u_{n-1} + A(u_n) = f$. Now this is an elliptic problem, and if I have appropriate properties on $A$ and $f$, I can use Crandall-Liggett. I will obtain a limit function $u$. The question is whether $u$ solves the PDE in some sense... | |
| Apr 1, 2014 at 21:05 | history | answered | András Bátkai | CC BY-SA 3.0 |