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

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