Timeline for Reference request: uniqueness for a certain PDE systems
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 21, 2019 at 21:49 | answer | added | Willie Wong | timeline score: 1 | |
| Nov 21, 2019 at 21:25 | comment | added | Daniele Tampieri | The fact that the equation for $v$ cannot be solved respect to the $t$ derivatives makes me think this is a problem of Sobolev type, i.e. (1) can be modeled as a Sobolev type equation: there are several monographs published on this topic. | |
| Nov 21, 2019 at 19:45 | comment | added | Ef_Ci | Hi @WillieWong . I am the author of the post but I had to write it as a guest because today I was having problems with the log in. The operators are of the form $L_i=-div(A_i\nabla u)$ with positive definite matrix. I have both boundary and initial conditions. | |
| Nov 21, 2019 at 17:19 | comment | added | Willie Wong | In particular, without boundary conditions, supposing that $L_2 v = 0$ has a non-trivial solution which we call $v_0$, then if you add $v \mapsto v + e^{-t} v_0$ this will also solve the equation. | |
| Nov 21, 2019 at 17:14 | comment | added | Willie Wong | When you say $L_1$ and $L_2$ are elliptic, which sign do you mean? (If you write $L_1 = \mathrm{div}(a \cdot \nabla u)$, is $a$ positive definite or negative definite?) Are you solving the boundary value problem , the initial value problem, or an initial-boundary value problem? | |
| Nov 21, 2019 at 14:45 | review | First posts | |||
| Nov 21, 2019 at 15:37 | |||||
| Nov 21, 2019 at 14:42 | history | asked | user148939 | CC BY-SA 4.0 |