Global solutions for dissipative Kirchhoff strings with non-Lipschitz nonlinear term
- 作者：Marina Ghisi
- 关键词：Hyperbolic equations ; Degenerate hyperbolic equations ; Dissipative equations ; Global existence ; Kirchhoff equations ; Asymptotic behaviour
- 刊名：Journal of Differential Equations
- 出版年：2006
- 期刊代码：74_00220396
- 类别：mt
- 出版时间：1 November 2006
- 卷：230
- 期：1
- 页码：128-139
- 文件大小：131 K
摘要
We investigate the evolution problem
where H is a Hilbert space, A is a self-adjoint nonnegative operator on H with domain D(A), δ>0 is a parameter, and m(r) is a nonnegative function such that m(0)=0 and m is nonnecessarily Lipschitz continuous in a neighborhood of 0.
We prove that this problem has a unique global solution for positive times, provided that the initial data (u0,u1)D(A)×D(A1/2) satisfy a suitable smallness assumption and the nondegeneracy condition . Moreover, we study the decay of the solution as t→+∞. These results apply to degenerate hyperbolic PDEs with nonlocal nonlinearities.