We consider the second order Cauchy problem for the Kirchhoff equation. It is well known that this problem admits local-in-time solutions provided that the initial data are regular enough, depending on the continuity modulus of the nonlinear term m. It is also well known that the solution is unique when m is locally Lipschitz continuous. In this paper we prove that if the initial data verify some algebraic condition, then the local solution is unique even if m is not Lipschitz continuous.

A uniqueness result for Kirchhoff equations with non-Lipschitz nonlinear term

GHISI, MARINA;GOBBINO, MASSIMO
2010-01-01

Abstract

We consider the second order Cauchy problem for the Kirchhoff equation. It is well known that this problem admits local-in-time solutions provided that the initial data are regular enough, depending on the continuity modulus of the nonlinear term m. It is also well known that the solution is unique when m is locally Lipschitz continuous. In this paper we prove that if the initial data verify some algebraic condition, then the local solution is unique even if m is not Lipschitz continuous.
2010
Ghisi, Marina; Gobbino, Massimo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/194805
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