COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Partial Differential Equations seminar > Scattering for wave equations with sources and slowly decaying data

## Scattering for wave equations with sources and slowly decaying dataAdd to your list(s) Download to your calendar using vCal - Hans Lindblad (Johns Hopkins)
- Monday 29 April 2024, 15:00-16:00
- MR13.
If you have a question about this talk, please contact Dr Greg Taujanskas. We construct solutions with prescribed radiation fields for wave equations with polynomially decaying sources close to the lightcone. In this setting, which is motivated by semilinear wave equations satisfying the weak null condition, solutions to the forward problem have a logarithmic leading order term on the lightcone and non-trivial homogeneous asymptotics in the interior of the lightcone. The backward scattering solutions we construct from knowledge of the source and the radiation field at null infinity alone are given to second order by explicit asymptotic solutions which satisfy novel matching conditions close to the light cone. This requires a delicate analysis close to the light cone of the forward solution with sources on the light cone. We also relate the asymptotics of the radiation field towards space-like infinity to explicit homogeneous solutions in the exterior of the light cone for slowly polynomially decaying data corresponding to mass, charge and angular momentum in the applications. The somewhat surprising discovery is that these data can cause the same logarithmic radiation field as the source term. This requires a delicate analysis of the forward homogeneous solution close to the light cone using the invertibility of the Funk transform. This is joint work with Volker Schlue. This talk is part of the Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- MR13
- My seminars
- Partial Differential Equations seminar
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsCambridge University United Nations Association (CUUNA) Topology Seminar Department of Chemistry## Other talksEnlightenment Theory of Rights Lunch Statistics Clinic Easter 2024 II Waves, oscillatory double integrals, and multidimensional complex analysis Curve Fitting, Errors and Analysis of Binding Data The Cahn-Hilliard-Navier-Stokes Framework for Multiphase Fluid Flows: Laminar, Turbulent, and Active |