Timeline for Uniqueness of solution of the wave equation
Current License: CC BY-SA 4.0
4 events
| when toggle format | what | by | license | comment | |
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| May 20, 2020 at 19:37 | comment | added | Willie Wong | @MKO: furthermore, the energy estimates can also be spatially localized due to finite speed of propagation; so if your worries are "growth at spatial infinity", you don't need to. See e.g. section 3 of my notes. | |
| May 20, 2020 at 19:36 | comment | added | Willie Wong | @MKO: the result also holds for distributional solutions. It is convenient to state it using your second version: if $\psi$ is a distribution on $\mathbb{R}^{1+n}$ that solves the linear wave equation in the distribution sense, and if the support of $\psi$ is disjoint from $\{t \leq 0\}$, then in fact $\psi$ is identically zero. | |
| May 20, 2020 at 19:30 | comment | added | asv | Thanks. It seems here you assume that some integrals converge (e.g. Sobolev norm is finite). This is interesting, but I am not sure this condition is satisfied in my situation. | |
| May 20, 2020 at 19:24 | history | answered | Bazin | CC BY-SA 4.0 |