Hyperbolic PDE and Conservation Laws
Wave equation, characteristics, shocks, and entropy solutions.
Hyperbolic PDE and Conservation Laws. Wave equation, characteristics, shocks, and entropy solutions.
Foundations and canonical references
The standard treatments of hyperbolic pde and conservation laws approach the subject from complementary angles. Dafermos, Hyperbolic Conservation Laws in Continuum Physics (2016) is the anchor reference for the subject and lays out the core definitions, theorems, and worked examples that practitioners return to. Evans, Partial Differential Equations (2010) gives a parallel, more proof-oriented exposition of the same material and is widely used as a graduate text.
Open methodological questions for hyperbolic pde and conservation laws include sharpening the bridges between foundational theory and computational practice, extending classical results to broader or more structured settings, and integrating the techniques surveyed above with adjacent mathematical disciplines. The references listed in this page are the entry points that current work builds on.
Prerequisites
Sources
- textbook · primary · 2016Hyperbolic Conservation Laws in Continuum Physicsdafermos-2016
- textbook · primary · 2010Partial Differential Equationsevans-2010
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