Mathematical Sciences: "Global Properties of Nonlinear Hyperbolic Equations Arising in Mathematical Physics"

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This project will investigate global properties of solutions to nonlinear hyperbolic equations arising in Mathematical Physics. In particular the PIs will consider nonlinear gravitational waves at large distances, formation of black holes, relation between gravitation and matter, stability of Minkowski space-time, and nonlinear Schrodinger equations in the critical case. The problems to be studied arise directly in Classical Field Theory, Continuum Mechanics, and General Relativity; their solutions will directly impact our basic understanding of matter and the universe.