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.File in questo prodotto:
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