论文标题
关于不可扩展，不可易换的粘弹性杆的自然曲率
On evolving natural curvature for an inextensible, unshearable, viscoelastic rod
论文作者
论文摘要
我们制定并考虑具有不断发展的自然构型，在平面上移动的不可延迟，不可理解的粘弹性杆的问题。我们证明，描述欧拉撑杆（无限尺寸动力学系统）的非静脉运动的动态方程式是全球范围良好的。对于端子推力的每个值，这些方程都包含静态溶液的平滑嵌入曲线（平衡点）。我们表征了关于任意平衡点的线性化方程的频谱，并使用此信息以及由于Brunovský和Polácik引起的动力学系统的收敛结果，我们证明，随着时间的无限度，运动对运动方程的每个解决方案都会收敛到平衡点。
We formulate and consider the problem of an inextensible, unshearable, viscoelastic rod, with evolving natural configuration, moving on a plane. We prove that the dynamic equations describing quasistatic motion of an Eulerian strut, an infinite dimensional dynamical system, are globally well-posed. For every value of the terminal thrust, these equations contain a smooth embedded curve of static solutions (equilibrium points). We characterize the spectrum of the linearized equations about an arbitrary equilibrium point, and using this information and a convergence result for dynamical systems due to Brunovský and Polácik, we prove that every solution to the quasistatic equations of motion converges to an equilibrium point as time goes to infinity.
