Stability and attractivity for a class of dissipative phenomena

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

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.

Qualitative properties for a class of non-autonomous semi-linear 3rd order PDE arising in dissipative problems

We improve results regarding the stability and attractivity of solutions $u$ of a large class of initial-boundary-value problems characterized by a semi-linear third order equation which may contain time-dependent coefficients. In the proof we use Liapunov functionals $W$ depending on two parameters, which we adapt to the 'error' $σ$.

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

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.

Existence, uniqueness and stability for a class of third order dissipative problems depending on time

We prove new results regarding the existence, uniqueness, (eventual) boundedness, (total) 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 Liapunov functional V depending on two parameters, which we adapt to the characteristics of the problem.

A unifying mechanical equation with applications to non-holonomic constraints and dissipative phenomena

A mechanical covariant equation is introduced which retains all the effectingness of the Lagrange equation while being able to describe in a unified way other phenomena including friction, non-holonomic constraints and energy radiation (Lorentz-Abraham-Dirac force equation). A quantization rule adapted to the dissipative degrees of freedom is proposed which does not pass through the variational formulation.

耗散的几何结构

The geometry of dissipation

本论文研究非保守动力学的几何建模框架，将保守系统的对称性、可积性等结果推广到耗散系统，分析了三类可分别刻画连续能量耗散与碰撞能量突变的几何框架。