Remarks on the Well-Posedness of the Nonlinear Cauchy Problem

Details Remarks on the Well-Posedness of the Nonlinear Cauchy Problem Remarks on the Well-Posedness of the Nonlinear Cauchy Problem

2006-11-14

arxiv.org/abs/math/0611441v1

Contemporary Mathematics 368 (2005) 337-356

Mathematics

Analysis of PDEs

Scientific paper

We show that hyperbolicity is a necessary condition for the well posedness of the noncharacteristic Cauchy problem for nonlinear partial differential equations. We give conditions on the initial data which are necessary for the existence of solutions and we analyze Hadamard's instabilities in Sobolev spaces. We also show that genuinely nonlinear equations raise new interesting problems.

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