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math.AP2025
Symmetric hyperbolic systems and shock waves
Satyanad Kichenassamy
The theory of symmetric-hyperbolic systems is useful for constructing smooth solutions of nonlinear wave equations, and for studying their singularities, including shock waves. We…
math.AP2025
Perimeter on a manifold, with applications to partial differential equations
Satyanad Kichenassamy
The perimeter of a measurable subset of is the total variation of its characteristic function. We generalize this notion to a subset of a closed Riemannian manifo…