Timeline for spaces of smooth functions for linear hyperbolic PDE
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
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| Sep 30, 2021 at 19:11 | comment | added | Igor Khavkine | @ArnoldNeumaier I've added an update, where I indicate how to handle the operator from your example. | |
| Sep 30, 2021 at 19:08 | history | edited | Igor Khavkine | CC BY-SA 4.0 |
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| Sep 29, 2021 at 13:58 | comment | added | Arnold Neumaier | I added an example to my question (correcting earlier comments here that were not completely correct). | |
| Sep 29, 2021 at 8:20 | comment | added | Igor Khavkine | @ArnoldNeumaier I understand what you mean by this kind of general hyperbolicity condition, but it's still not clear to me what class of systems you are referring to. Maybe you could add an example or an explanation to the original question. | |
| Sep 29, 2021 at 8:06 | comment | added | Arnold Neumaier | Independent of the order of the principal symbol, a hyperbolic system can be defined in terms of the microlocal spectrum at each point. It should consist of timelike and antitimelike but not of spacelike directions with respect to some cone. | |
| Sep 28, 2021 at 20:57 | comment | added | Igor Khavkine | @ArnoldNeumaier I'm not sure what you mean by "semidefinite". In what sense would such a system be hyperbolic? | |
| Sep 27, 2021 at 20:41 | comment | added | Arnold Neumaier | The 2015 paper of Bär is the kind of results I wanted to see. But another case of interest for me is a system of first oder equations where the symbol is only semidefinite in future-directed directions. Are there results generalizing Bär's Theorem 5.8 in this case, with additional assumptions on the differential operator\ | |
| Sep 27, 2021 at 20:36 | vote | accept | Arnold Neumaier | ||
| Sep 27, 2021 at 13:59 | comment | added | Arnold Neumaier | Thanks! I'll study these references to see whether they answer my question. | |
| Sep 27, 2021 at 12:57 | history | answered | Igor Khavkine | CC BY-SA 4.0 |