Timeline for BV functions and wave equation
Current License: CC BY-SA 4.0
7 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 22, 2019 at 21:20 | vote | accept | Riku | ||
| Apr 22, 2019 at 21:18 | comment | added | Willie Wong | @Riku: a wave equation is a particular form of a conservation law. For example, if you write $-\partial_t^2 \phi + \partial^2_x\phi = 0$ for the linear wave equation, and set $\psi_1 = \partial_t \phi$ and $\psi_2 = \partial_x \phi$, then the wave equation is equivalent to the conservation laws $\partial_t \psi_1 - \partial_x \psi_2 = 0$ coupled to $\partial_t \psi_2 - \partial_x \psi_1 = 0$. | |
| Apr 22, 2019 at 21:17 | comment | added | Riku | @WillieWong In fact, why is the answer talking about entropy solutions? | |
| Apr 22, 2019 at 21:16 | comment | added | Riku | @WillieWong Isn't book of Bressan about conservation laws and not about wave equations? | |
| Apr 22, 2019 at 21:15 | comment | added | Willie Wong | @Riku: the one dimensional case is described in A. Bressan, Hyperbolic Systems of Conservation Laws. The One Dimensional Cauchy Problem. Oxford University Press, Oxford, 2000. The result of Rauch referred to is Commun. Math. Phys. 106, 481--484 (1986). | |
| Apr 22, 2019 at 20:56 | comment | added | Riku | This is very interesting. Thank you. Could you add some references for the claims regarding the one-dimensional case? | |
| Apr 22, 2019 at 19:32 | history | answered | Denis Serre | CC BY-SA 4.0 |