标题： 一类依赖于时间的三阶耗散问题的存在性、唯一性和稳定性 显示英文标题

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

摘要： 我们证明了关于一类具拟线性三阶方程（该方程可能含有时间相关系数）的初边值问题解的存在性、唯一性、（最终）有界性、（完全）稳定性和吸引性的新结果。 这类方程包括超导理论和粘弹性材料理论中出现的方程。 在证明过程中，我们使用了一个依赖于两个参数的李雅普诺夫泛函 \( V \)，并根据问题的特点对其进行调整。 显示英文摘要

摘要： 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.