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Questions on partial (as opposed to ordinary) differential equations.

Partial equations contain partial derivatives and usually contain two or more variables; the single-variable cases with normal derivatives are ordinary differential equations. Questions with this tag may be about, among others:

  1. Analysis of existence and uniqueness of classical/strong/weak/viscous/etc solutions in boundary value problems/Cauchy problems/Riemann problems.
  2. Functional analysis related to PDE, e.g., theories of Sobolev spaces, Bochner spaces, analysis of linear/nonlinear differential operators and pseudodifferential operators, etc.
  3. The stability, long-term behavior of the solution.
  4. Different methods of solving PDEs, separation of variables, Fourier transform, solitons, method of characteristics.
  5. The solution technique of the Euler-Lagrange equations from calculus of variations.
  6. Equation-relevant theory in other fields, e.g. Hyperbolic conservation laws in fluid/gas dynamics, Maxwell's equations in electromagnetism, Hamilton-Jacobi equation in control theory, etc.

Please consider using more specific tags if your question addresses some of the aspects in that field, e.g., , , , , , .

Reference: L. C. Evans, Partial Differential Equations.

See also Wikipedia and MathWorld entries.

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