Partial differential equations Basic notions and classification Concept
Hyperbolic partial differential equation
Summary
A hyperbolic partial differential equation is an evolution equation whose Cauchy problem is well posed for data on suitable hypersurfaces. Disturbances travel at finite speed. The model case is the wave equation. Hyperbolic equations describe waves, vibrations and the transport of conserved quantities, and singularities of the data propagate along characteristics instead of being smoothed out. See the definition.
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About this page
| Tag | 92C3S03AQZ |
|---|---|
| URI | m2://92C3S03AQZ |
| Kind | concept |
| Writing | W0 stub |
| MSC | 35L10, 35L25 |
| Specializes | Partial differential equation |
| Same as | |
| Changed | 2 November 2026 |
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Special cases
Used by
- Tricomi equation
- Finite speed of propagation
- Telegrapher's equations
- Klein–Gordon equation
- Mixed-type equation
- Christodoulou–Klainerman stability of Minkowski space
- Wave equation
- Strict hyperbolicity
- Hyperbolic conservation law