6 1. INTRODUCTION
1.2.2. Systems of partial differential equations.
a. Linear systems.
1. Equilibrium equations of linear elasticity
μΔu + (λ + μ)D(div u) = 0.
2. Evolution equations of linear elasticity
utt − μΔu − (λ + μ)D(div u) = 0.
3. Maxwell’s equations
⎧
⎨
⎩
Et = curl B
Bt = − curl E
div B = div E = 0.
b. Nonlinear systems.
1. System of conservation laws
ut + div F(u) = 0.
2. Reaction-diffusion system
ut − Δu = f(u).
3. Euler’s equations for incompressible, inviscid flow
ut + u · Du = −Dp
div u = 0.
4. Navier–Stokes equations for incompressible, viscous flow
ut + u · Du − Δu = −Dp
div u = 0.
See Zwillinger [Zw] for a much more extensive listing of interesting PDE.
1.3. STRATEGIES FOR STUDYING PDE
As explained in §1.1 our goal is the discovery of ways to solve partial differ-
ential equations of various sorts, but—as should now be clear in view of the
