Abstract
In this talk we will review some results from the theory of partial differential equations in order to approach the study and analysis of the initial value problem of certain classical field theories in Physics, particularly in the framework of General Relativity. After reviewing the pseudodifferential theory of first order systems and some results on hyperbolicity, we will see how certain nonlinear extensions of classical theories in Physics such as Electromagnetism and Hydrodynamics can be turned to be hyperbolic, and under which requeriments it is possible to guarantee a well-posed initial value formulation.
Well-Posedness Results on Non-Linear Classical Field Theories in Physics
In this talk we will review some results from the theory of partial differential equations in order to approach the study and analysis of the initial value problem of certain classical field theories in Physics, particularly in the framework of General Relativity. After reviewing the pseudodifferential theory of first order systems and some results on hyperbolicity, we will see how certain nonlinear extensions of classical theories in Physics such as Electromagnetism and Hydrodynamics can be turned to be hyperbolic, and under which requeriments it is possible to guarantee a well-posed initial value formulation.
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