Abstract 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.

中文翻译：

---

一维应变限制粘弹性初值问题解的局部存在性

摘要 在这项工作中，我们证明了一维应变限制粘弹性中出现的初值问题的强解的局部存在性，该问题基于线性化应变、线性化应变变化率和线性化应变之间的非线性本构关系。压力。该模型是非线性 Kelvin-Voigt 粘弹性固体在应变和应变率较小的假设下的推广。我们为应力变量定义了一个初值问题，然后在非线性本构函数严格递增的假设下，我们将问题转换为应变和应变率之和的新形式。使用变系数热方程理论和不动点论证，我们证明了解的局部存在性。最后，