Timeline for Solving the Moutard PDE
Current License: CC BY-SA 4.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 24 at 14:06 | comment | added | RWien | @DeaneYang the link just redirects into a login page of a NYU account. If you name the paper I can obtain it using my uni account. | |
| May 24 at 13:13 | comment | added | Deane Yang | Yes. You cannot get it through your university? | |
| May 24 at 6:07 | comment | added | RWien | @DeaneYang thank you for the clarification but the link you provided is not working. It is jumping to a log in page. | |
| May 23 at 18:59 | comment | added | Deane Yang | A discussion of how to solve using inverse scattering techniques the Goursat problem for the sine-Gordon equation can be found here: epubs-siam-org.proxy.library.nyu.edu/doi/abs/10.1137/0134004 | |
| May 23 at 18:58 | comment | added | Deane Yang | By $u=c$, I mean any line parallel to $u=0$. $c$ is just an arbitrary constant. As @IgorKhavkine points out these lines are characteristic "surfaces", so standard initial value problems do not apply. | |
| May 23 at 17:32 | comment | added | RWien | @IgorKhavkine Isn't it like this that for this problem the characteristics lines are the ones that are parallel to $u$ and $v$ axes? Therefore my initialization which is on $(u,0)$ and $(0,v)$ should not work right? or am I misled somewhere? | |
| May 23 at 13:15 | comment | added | RWien | @IgorKhavkine I think you pointed me to a very helpful reference. Thanks for the 2nd time helping me with my PDEs. | |
| May 23 at 10:29 | comment | added | Igor Khavkine | Classically this type of boundary value problem is called a "Goursat problem" (the boundaries where the data is provided are so-called characteristic curves (codim-1 surfaces really), as pointed out by Deane). Some quick searching for "2d Goursat problem" turns up this chapter from a book by Rubinstein & Rubinstein (1994). | |
| May 23 at 6:42 | comment | added | RWien | @DeaneYang I did not understand what you mean by $u =c$ and $v =c$. what is $c$ here? | |
| May 23 at 3:40 | comment | added | Deane Yang | You should look up the literature on the sine-Gordon equation. The techniques for solving it should apply just as well to your equation. Your question is not about the standard initial value problem for the equation but for characteristic initial data ($u=c$ and $v=c$ are characteristic curves of the equation). So you should look for that. | |
| May 22 at 18:46 | comment | added | RWien | @ResearchMath I added some extra info. | |
| May 22 at 18:45 | history | edited | RWien | CC BY-SA 4.0 |
Added details based on the request of a user.
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| May 22 at 15:37 | comment | added | ResearchMath | Is that really all you know about $q$? If you have more information about $q$ it might make it easier. | |
| May 22 at 11:40 | history | asked | RWien | CC BY-SA 4.0 |