Questions on "Partial Differential Equations", as opposed to "ordinary differential equations".
The theory and application of equations relating multivariate function and their partial derivatives. The questions tagged with this tag can be about, but not limited to:
- Analysis of existence and uniqueness of classical/strong/weak/viscous/etc solutions in boundary value problems/Cauchy problems/Riemann problems.
- Functional analysis related to PDE, e.g., theories of Sobolev spaces, Bochner spaces, analysis of linear/nonlinear differential operators and pseudodifferential operators, etc.
- The stability, long time behavior of the solution.
- Different methods of solving PDEs, separation of variables, Fourier transform, solitons, method of characteristcs.
- The solution technique of the Euler-Lagrange equations from calculus of variations.
- Equation-relevant theory in other fields, e.g. Hyperbolic conservation laws in fluid/gas dynamics, Maxwell's equations in electromagnetics, 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., functional-analysis, calculus-of-variations, operator-theory, physics, fluid-dynamics, sobolev-spaces.
Reference: L.C.Evans, Partial Differential Equations.