Timeline for First order partial differential equation
Current License: CC BY-SA 4.0
3 events
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| Mar 24, 2019 at 11:33 | comment | added | Bazin | Yes, it is a general fact for a first-order scalar PDE, which is in fact equivalent to a system of ODE. Lipschitz-continuity is a sufficient condition to get a proper definition for the flow $\phi$ above, but it is not necessary: looking at a system of ODE $\dot x=v(x)$, it is enough to know that $v\in W^{1,1}$ with a bounded divergence to get a flow. The latter situation was studied by P.L. Lions \& R. DiPerna. | |
| Mar 24, 2019 at 4:00 | comment | added | user135936 | So you say that assuming that $v(x)$ is Lipschitz then the solution of this PDE with given initial condition is unique? | |
| Mar 23, 2019 at 18:24 | history | answered | Bazin | CC BY-SA 4.0 |