Separable motions for self-gravitating hyperelastic matter

Juhi Jang; Trevor M. Leslie; Juhi Jang; Trevor M. Leslie

doi:10.3934/cam.2025032

Communications in Analysis and Mechanics

2025, Volume 17, Issue 3: 810-828. doi: 10.3934/cam.2025032

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Separable motions for self-gravitating hyperelastic matter

Juhi Jang ¹,
Trevor M. Leslie ^{2
,
,}

1.
Department of Mathematics, University of Southern California, Los Angeles, CA 90089, USA
2.
Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL 60616, USA

Received: 30 December 2024 Revised: 09 April 2025 Accepted: 30 May 2025 Published: 04 September 2025
35Q74, 35A09, 74B99, 35K20

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.
- hyperelastic matter,
- self-gravitation,
- separable/homologous solutions,
- strain energy,
- solid vacuum boundary conditions
Citation: Juhi Jang, Trevor M. Leslie. Separable motions for self-gravitating hyperelastic matter[J]. Communications in Analysis and Mechanics, 2025, 17(3): 810-828. doi: 10.3934/cam.2025032

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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.

References

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