论文标题
局部存在用于一维应变粘弹性的初始值问题的解决方案
Local existence of solutions to the initial-value problem for one-dimensional strain-limiting viscoelasticity
论文作者
论文摘要
在这项工作中，我们证明了在一维应变限制粘弹性中产生的初始值问题的局部解决方案，该粘弹性基于线性化菌株之间的非线性组成型关系，线性化应变的变化速率和应力。在假设应变和应变速率很小的假设下，该模型是非线性开尔文 - VOIGT粘弹性固体的概括。我们为应力变量定义了一个初步问题问题，然后在严格增加非线性本构函数的假设下，我们将问题转换为应变和应变速率之和的新形式。使用可变系数热方程的理论以及固定点参数，我们证明了解决方案的局部存在。最后，对于文献中广泛使用的几种本构函数，我们表明，存在证明所基于的假设并未违反。
In this work we prove local existence of strong solutions to the initial-value problem arising in one-dimensional strain-limiting viscoelasticity, which is based on a nonlinear constitutive relation between the linearized strain, the rate of change of the linearized strain and the stress. The model is a generalization of the nonlinear Kelvin-Voigt viscoelastic solid under the assumption that the strain and the strain rate are small. We define an initial-value problem for the stress variable and then, under the assumption that the nonlinear constitutive function is strictly increasing, we convert the problem to a new form for the sum of the strain and the strain rate. Using the theory of variable coefficient heat equation together with a fixed point argument we prove local existence of solutions. Finally, for several constitutive functions widely used in the literature we show that the assumption on which the proof of existence is based is not violated.
