Timeline for Existence and Uniqueness of Solutions to Quasilinear Parabolic PDEs
Current License: CC BY-SA 3.0
12 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Oct 26, 2017 at 6:59 | comment | added | Chee Han | @AnthonyCarapetis Great, I will check it out tomorrow when I have the time. Thank you so very much! | |
| Oct 26, 2017 at 6:50 | comment | added | Anthony Carapetis | Yes, that's right - don't let the title put you off, the chapter is largely about applying fixed point theorems to get existence results for nonlinear equations. | |
| Oct 26, 2017 at 6:48 | comment | added | Chee Han | @AnthonyCarapetis Chapter 8 turns out to be fixed point theorems, unless I am looking at the wrong book. The book is "Second Order Parabolic DEs"? | |
| Oct 26, 2017 at 5:32 | comment | added | Anthony Carapetis | OK, that makes more sense. I believe that with the right assumptions on $g$, you should be able to reference chapter 8 of Lieberman for the existence (see the section on oblique derivative problems) and chapter 9 for the uniqueness. | |
| Oct 26, 2017 at 5:25 | comment | added | Chee Han | @AnthonyCarapetis You are absolutely right. It was supposed to be Neumann instead of Dirichlet boundary conditions. I have edited the question. | |
| Oct 26, 2017 at 5:24 | history | edited | Chee Han | CC BY-SA 3.0 |
Typos.
|
| Oct 26, 2017 at 4:17 | comment | added | Anthony Carapetis | Should it really be $g(u(x,t))$ and not just $g(x,t)$? As written it's some kind of weird fixed-point condition that is certainly not well-posed for all $g$ (e.g. $g = \mathrm id$ makes the boundary condition vacuous). | |
| Oct 26, 2017 at 4:14 | comment | added | Chee Han | @AnthonyCarapetis It should be $u(x,t)$, unless you meant otherwise? | |
| Oct 26, 2017 at 4:13 | history | edited | Chee Han | CC BY-SA 3.0 |
Typos
|
| Oct 26, 2017 at 3:36 | comment | added | Anthony Carapetis | I'm not sure I understand the boundary condition - is there a typo? | |
| Oct 26, 2017 at 2:42 | history | edited | Chee Han | CC BY-SA 3.0 |
Edit title.
|
| Oct 26, 2017 at 1:31 | history | asked | Chee Han | CC BY-SA 3.0 |