arXiv 0807.51072008-07-31math-phmath.MP

Stability properties for some non-autonomous dissipative phenomena proved by families of Liapunov functionals

Armando D'Anna, Gaetano Fiore

备注：: Latex file, 12 pages
发表信息：: Nonlinear Dyn. Syst. Theory 9 (2009), 249-262

英文摘要：

We prove some new results regarding the boundedness, stability and attractivity of the solutions of a class of initial-boundary-value problems characterized by a quasi-linear third order equation which may contain time-dependent coefficients. The class includes equations arising in Superconductor Theory, and in the Theory of Viscoelastic Materials. In the proof we use a family of Liapunov functionals W depending on two parameters, which we adapt to the `error', i.e. to the size of the chosen neighbourhood of the null solution.

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