Existence and asymptotic stability for evolution problems on manifolds with damping and source terms
Existence and asymptotic stability for evolution problems on manifolds with damping and source terms
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DOI：
10.1016/j.jmaa.2003.10.020
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发表时间：
2004-03
影响因子：
1.3
通讯作者：
M. Cavalcanti;V. Cavalcanti
中科院分区：
文献类型：
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作者：
M. Cavalcanti;V. Cavalcanti
一个考虑具有源和阻尼项的非线性演化方程[公式：见文本]，其中Γ是紧致流形。利用势井法证明了解的整体存在性。此外，我们采用Patrick Martinez在ESAIM控制优化中引入的思想研究了解的渐近行为。当流形上的摩擦阻尼机构g在原点附近不一定有多项式增长时，Calc. Var. 4(1999) 419-444。
One considers the nonlinear evolution equation with source and damping terms [Formula: see text] where Γ is a compact manifold. We prove the global existence of solutions making use of the potential well method. Furthermore, we study the asymptotic behaviour of solutions adapting the ideas introduced by Patrick Martinez in ESAIM Control Optim. Calc. Var. 4 (1999) 419–444 when the frictional damping mechanism g on the manifold does not necessarily have a polynomial growth near the origin.