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.