Remarks on the Well-Posedness of the Nonlinear Cauchy Problem
Language
en
Article de revue
This item was published in
Contemporary mathematics. 2005, vol. 368, p. 337-356
American Mathematical Society
English Abstract
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 ...Read more >
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.Read less <
English Keywords
Cauchy Problem
well posedness
Hadamard's instability
Origin
Hal imported