A Mixture With Local Kelvin-Voigt Damping

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A Mixture With Local Kelvin-Voigt Damping

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2020-02

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In this paper, we will further explore a theory of viscoelastic mixtures proposed by [Iesan, 2004] and analyzed by [Quintanilla, 2005]. In the first of these papers, the author Iesan introduced a theory for a mixture between a viscoelastic material and an elastic material. In this theory, the dissipation effects are determined by the viscosity of rate type of a constituent and the relative velocity. [Quintanilla, 2005] states the linear equations of the thermomechanical deformations. Then, he studies several qualitative properties such as well-posedness and exponential stability. An important result of the paper of [Quintanilla, 2005] is a proof of exponential decay of solution when only one of the dissipative mechanisms is present in the case of anti-shear deformations. We concentrate our attention on a similar case where only one of the dissipative mechanisms is present and is localized. This means that the dissipation can be zero in a part of the domain, but have positive measure support.

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University of Minnesota M.S. thesis. February 2020. Major: Mathematics. Advisor: Zhuangyi Liu. 1 computer file (PDF); ii, 43 pages.

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Crenshaw, Aaron. (2020). A Mixture With Local Kelvin-Voigt Damping. Retrieved from the University Digital Conservancy, https://hdl.handle.net/11299/214984.

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