Partial differential equations Basic notions and classification Concept
Linear PDE
Summary
A linear PDE is a partial differential equation in which the unknown and its derivatives appear only linearly. Its coefficients depend on the variables alone. For a linear homogeneous equation, sums and multiples of solutions are again solutions. This superposition principle makes linear PDEs the best understood class, and it is the setting of Fourier methods, fundamental solutions and distribution theory. See the definition.
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| Tag | 6DZETZ5T9G |
|---|---|
| URI | m2://6DZETZ5T9G |
| Kind | concept |
| Writing | W0 stub |
| MSC | 35A99 |
| Specializes | Semilinear PDE |
| Changed | 2 November 2026 |
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Used by
- Holmgren's uniqueness theorem
- Malgrange–Ehrenpreis theorem
- Elliptic partial differential equation
- Local solvability
- Classification of second-order PDEs
- Characteristic variety
- Principal symbol
- Parabolic partial differential equation
- Hyperbolic partial differential equation
- Fundamental solution