Concepts of Hyperbolicity and Relativistic Continuum Mechanics
Robert Beig
TL;DR
This paper reviews the geometric concepts of hyperbolicity in PDEs, focusing on symmetric and regular hyperbolicity, with examples from continuum mechanics, to deepen understanding of relativistic and nonrelativistic systems.
Contribution
It provides a comprehensive review of hyperbolicity notions in PDEs with applications to continuum mechanics, highlighting their geometric foundations and examples.
Findings
Symmetric hyperbolicity ensures well-posedness of first-order systems.
Regular hyperbolicity applies to second-order systems in continuum mechanics.
Numerous examples illustrate the application of hyperbolicity concepts.
Abstract
After a short introduction to the characteristic geometry underlying weakly hyperbolic systems of partial differential equations we review the notion of symmetric hyperbolicity of first-order systems and that of regular hyperbolicity of second-order systems. Numerous examples are provided, mainly taken from nonrelativistic and relativistic continuum mechanics.
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.