Global Stability properties for a class of dissipative phenomena via one or several Liapunov functionals

Abstract

We find some new results regarding the existence, uniqueness, 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 have non-autonomous forcing terms. The class includes equations arising in Superconductor Theory, Quantum Mechanics and in the Theory of Viscoelastic Materials.

arXiv commentLatex file, 30 pages. To appear in "Nonlinenar Dynamics and System Theory"

Cited by in corpus (5)

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• On kinks and other travelling-wave solutions of a modified sine-Gordon equation
• Towards soliton solutions of a perturbed sine-Gordon equation
• Existence, uniqueness and stability for a class of third order dissipative problems depending on time
• Stability properties for some non-autonomous dissipative phenomena proved by families of Liapunov functionals