Bounded time inverse scattering for nonlinear Dirac equation (Joint w/ IP seminar)

Yuchao Yi, UCSD
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PDL C-038

Consider a semilinear Dirac equation with some smooth
non-linearity F(u), and suppose the solution can be observed at some
fixed time T for any sufficiently small initial data. We call the map
that maps initial data at time 0 to solution at time T the bounded
time scattering map, and ask if this map uniquely determines the
non-linearity. In this talk, I will show that if the first and second
derivatives of the non-linearity at 0 are given, then the
non-linearity can be uniquely determined on a bounded region around 0,
where the size of the region depends on the available set of initial
data. The proof relies on higher order linearization, microlocal
analysis, and a limiting argument for the collision point. A similar
result can be obtained when the non-linearity also depends on the
space variable (but independent of time).

 
 

 

 
 
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