Decay of solutions for strain gradient mixtures. Issue 2 (14th November 2022)

• Record Type: Journal Article
• Authors: Magaña, Antonio; Magaña, Marc; Quintanilla, Ramon
• Is Part Of: Zeitschrift für angewandte Mathematik und Mechanik. Volume 103:Issue 2(2023)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2022-11-14
• Subjects: Mathematics -- Periodicals; Mechanics, Applied -- Periodicals; Engineering -- Periodicals; 519
• DOI: 10.1002/zamm.202200089
• Languages: English
• ISSNs: 0044-2267

Abstract

Abstract: We study antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin‐Voigt type in a cylinder. Our aim is to analyze the behaviour of the solutions with respect to the time variable when a dissipative structural mechanism is considered. We study three different cases, each at a time. For each case we prove existence and uniqueness of solutions. We obtain the exponential decay of the solutions in the hyperviscosity and viscosity cases. Exponential decay is also expected when the dissipation is generated by the relative velocity (in the generic case, although a particular combination of the constitutive parameters leads to slow decay). These results are proved with the help of the theory of semigroups. Abstract : We study antiplane shear deformations for isotropic and homogeneous strain gradient mixtures of the Kelvin‐Voigt type in a cylinder. Our aim is to analyze the behaviour of the solutions with respect to the time variable when a dissipative structural mechanism is considered. We study three different cases, each at a time. For each case we prove existence and uniqueness of solutions. We obtain the exponential decay of the solutions in the hyperviscosity and viscosity cases.…