Timeline for Existence of solution to nonlinear first order PDE with C^1 bounds
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 4 at 20:33 | vote | accept | JMK | ||
| Feb 3 at 8:22 | history | edited | Daniele Tampieri | CC BY-SA 4.0 |
Minor Formatting
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| Feb 3 at 2:27 | answer | added | Willie Wong | timeline score: 3 | |
| Feb 3 at 1:58 | comment | added | Willie Wong | So technically speaking your equation is not even a PDE (it is nonlocal); I am not convinced by the "hyperbolic-pde" tag in this case. (Did you mess up $p$s and $q$s in your definition of $P(v,q)$?) | |
| Feb 2 at 17:49 | history | edited | JMK | CC BY-SA 4.0 |
Changed example
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| Feb 2 at 17:45 | comment | added | JMK | Hi @WillieWong, unfortunately it really is a Dirichlet-to-Neumann operator so I'm not sure if there's more dependence. If useful, I'm looking at $\partial_{\nu} u$ where $u = (-\Delta + 1)^{-1} (P(D^2f, Df))$. I think $P= P(v,q) = a^{i} v_i + b^j p_j + c^{ij} v_i p_j$ though. Does this help? | |
| Feb 2 at 2:45 | comment | added | Willie Wong | The generalization to $k = 2$ certainly won't work, since the reverse-time heat equation falls into that category. // Also, can you be a bit more precise on what $F$ depends on? Is $F: \mathbb{R}\to\mathbb{R}$ and you literally plugging in $F\circ f$, or is the notation $F(f(p,t))$ more of a functional dependence? The example you gave in the bottom using the Dirichlet to Neumann operator cannot be really written as $F(f)$. | |
| Feb 1 at 23:54 | history | edited | JMK | CC BY-SA 4.0 |
added 46 characters in body
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| Feb 1 at 22:44 | history | asked | JMK | CC BY-SA 4.0 |