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A Cauchy Problem with Singularity Along the Initial Hypersurface
Hanson-Hart, Zachary Aaron
Hanson-Hart, Zachary Aaron
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Thesis/Dissertation
Date
2011
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Mathematics
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http://dx.doi.org/10.34944/dspace/1370
Abstract
We solve a one-sided Cauchy problem with zero right hand side modulo smooth errors for the wave operator associated to a smooth symmetric 2-tensor which is Lorentz on the interior and degenerate at the boundary. The degeneracy of the metric at the boundary gives rise to singularities in the wave operator. The initial data prescribed at the boundary must be modified from the classical Cauchy problem to suit the problem at hand. The problem is posed on the interior and the local solution is constructed using microlocal analysis and the techniques of Fourier Integral Operators.
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