2025/06/02 by Juhi Jang, Jang, Juhi, Trevor M. Leslie +1
Engineering · Physics and Astronomy · #Analysis of PDEs (math.AP) #Elasticity and Material Modeling #Elasticity and Wave Propagation #FOS: Mathematics #Planetary Science and Exploration
paper · pdf · doi:10.48550/arxiv.2506.02278
openalex publication_date 2025/06/02 · openalex created_date 2025/10/14 · openalex updated_date 2026/07/28
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.