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Inversion of Non-uniform Difference Operators
PDE and Applied Math Seminar| Speaker: | Robin Young, University of Massachusetts, Amherst, |
| Related Webpage: | young@math.umass.edu |
| Location: | zoom zoom |
| Start time: | Tue, Jan 11 2022, 4:10PM |
We introduce and solve the problem of inverting a non-uniform
difference operator, or equivalently of solving the (linear)
difference equation
$$ \Delta_\Phi\big[v\big](t) := v\big(\Phi(t)\big) - v(t) = w(t),$$
with uniform bounds on the solution operator; here $\Phi$ is a given
invertible map of the circle. This is the simplest form of an
equation that arises in our long-term project of proving the existence
of time- and space-periodic solutions of the compressible Euler
equations of fluid dynamics. Obtaining bounds on the solution
operator with a finite loss of derivatives is an essential step in
applying the Nash-Moser method to this larger problem. We solve
the problem in stages, depending on the geometric structure of the
shift map $\Phi$. After identifying a solvability condition, we are able
to completely characterize the solution operator and obtain bounds.
We end with a discussion of the ways we expect to apply these
techniques in our Nash-Moser iteration.
This is joint work with Blake Temple.
J Temple is inviting you to a scheduled Zoom meeting. Topic: Applied Math/PDE Seminar Time: This is a recurring meeting Meet anytime Join Zoom Meeting https://ucdavis.zoom.us/j/94069828548?pwd=UWsvdjk0NXVRVXRJUVdjZFJ5VUVjQT09 Meeting ID: 940 6982 8548 Passcode: 210427 One tap mobile +16699006833,,94069828548#,,,,*210427# US (San Jose) +12532158782,,94069828548#,,,,*210427# US (Tacoma) Dial by your location +1 669 900 6833 US (San Jose) +1 253 215 8782 US (Tacoma) +1 346 248 7799 US (Houston) +1 301 715 8592 US (Washington DC) +1 312 626 6799 US (Chicago) +1 646 876 9923 US (New York) Meeting ID: 940 6982 8548 Passcode: 210427 Find your local number: https://ucdavis.zoom.us/u/aXu24KKjK Join by SIP 94069828548@zoomcrc.com Join by H.323 162.255.37.11 (US West) 162.255.36.11 (US East) 115.114.131.7 (India Mumbai) 115.114.115.7 (India Hyderabad) 213.19.144.110 (Amsterdam Netherlands) 213.244.140.110 (Germany) 103.122.166.55 (Australia Sydney) 103.122.167.55 (Australia Melbourne) 64.211.144.160 (Brazil) 69.174.57.160 (Canada Toronto) 65.39.152.160 (Canada Vancouver) 207.226.132.110 (Japan Tokyo) 149.137.24.110 (Japan Osaka) Meeting ID: 940 6982 8548 Passcode: 210427