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Research Article | Open Access

Separable motions for self-gravitating hyperelastic matter

Juhi Jang1, Trevor M. Leslie2( )
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA
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Abstract

In this paper, we prove the existence of separable solutions to the equations of motion for self-gravitating hyperelastic matter, under an appropriate class of constitutive assumptions on the strain-energy function. Our framework includes both global-in-time solutions which expand and also solutions which collapse to a point in finite time. Other authors have constructed expanding solutions in similar settings, but to the best of our knowledge, the collapsing solutions we construct are completely new.

Keywords

hyperelastic matterself-gravitationseparable/homologous solutionsstrain energysolid vacuum boundary conditions
CLC number: 35Q74, 35A09, 74B99, 35K20

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Communications in Analysis and Mechanics
Volume 17 Issue 3,
September 2025
Pages 810-828
DOI: 10.3934/cam.2025032

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Cite this article:
Jang J, Leslie TM. Separable motions for self-gravitating hyperelastic matter. Communications in Analysis and Mechanics, 2025, 17(3): 810-828. https://doi.org/10.3934/cam.2025032

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Received: 30 December 2024
Revised: 09 April 2025
Accepted: 30 May 2025
Published: 15 September 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)