We consider the mildly degenerate Kirchhoff equation with a dissipative term. We prove that if the nonlinear term is locally Lipschitz continuous and the initial data are small enough then the Cauchy problem is globally well-posed for positive times. Moreover, we study the asymptotic behavior of the solutions.

Global Existence and Asymptotic Behaviour for a Mildly Degenetate Dissipative Hyperbolic Equation of Kirchhoff Type

GHISI, MARINA;GOBBINO, MASSIMO
2004-01-01

Abstract

We consider the mildly degenerate Kirchhoff equation with a dissipative term. We prove that if the nonlinear term is locally Lipschitz continuous and the initial data are small enough then the Cauchy problem is globally well-posed for positive times. Moreover, we study the asymptotic behavior of the solutions.
2004
Ghisi, Marina; Gobbino, Massimo
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11568/91411
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