Mathematical Sciences: Linear and Nonlinear Hyperbolic Problems

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The principal investigator will study a variety of problems concerning the qualitative properties of the solutions of partial differential equations which describe nonlinear wave motion. In particular, an investigation will be made of the propagation of singularities of solutions along caustics and to study linear inverse hyperbolic problems like determining the speed of sound from information given by the problem. The qualitative analysis of nonlinear waves is of significant scientific interest in view of their wide spread occurrence in real world situations.