Timeline for $|\nabla \omega|^2= \alpha \omega^n+ \beta$ - References
Current License: CC BY-SA 4.0
13 events
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Nov 30, 2018 at 16:46 | comment | added | MathDG | Let us continue this discussion in chat. | |
Nov 30, 2018 at 15:41 | comment | added | Willie Wong | In that case, it may be worthwhile to include in your question some discussion of where this equation comes from and why you cannot do the nonlinear change of variables that I suggested, to get a more targeted response. | |
Nov 30, 2018 at 15:16 | comment | added | MathDG | @Willie Wong - thank you very much for the suggestion but unfortunately I can not transform it | |
Nov 30, 2018 at 15:07 | history | edited | YCor | CC BY-SA 4.0 |
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Nov 30, 2018 at 14:42 | comment | added | Willie Wong | Actually, can you not transform this into a standard eikonal equation? If you let $F:\mathbb{R}\to\mathbb{R}$ be a primitive of $(\alpha z^n + \beta)^{-\frac12}$, then your equation is equivalent to $|\nabla F(\omega)| = 1$ which is the standard eikonal equation. | |
Nov 30, 2018 at 14:36 | comment | added | MathDG | @Willie Wong - Thank you very much! | |
Nov 30, 2018 at 14:33 | comment | added | Willie Wong | It looks like an eikonal equation with a nonlinear wave speed; that's what I would search for anyway as a start. | |
Nov 30, 2018 at 13:47 | comment | added | MathDG | @Piotr Hajlasz - Yes, there was a mistake, thank you! | |
Nov 30, 2018 at 13:45 | history | edited | MathDG | CC BY-SA 4.0 |
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Nov 30, 2018 at 13:31 | comment | added | Piotr Hajlasz | I do not understand it. From the equation you get that $\omega=(-\beta/\alpha)^{1/n}$ is constant. There must be a mistake in your statement. | |
Nov 30, 2018 at 12:46 | history | undeleted | MathDG | ||
Nov 30, 2018 at 12:45 | history | deleted | MathDG | via Vote | |
Nov 30, 2018 at 12:37 | history | asked | MathDG | CC BY-SA 4.0 |