1.2. EXAMPLES 5
b. Nonlinear equations.
1. Eikonal equation
|Du| = 1.
2. Nonlinear Poisson equation
−Δu = f(u).
3. p-Laplacian equation
div(|Du|p−2Du)
= 0.
4. Minimal surface equation
div
Du
(1 +
|Du|2)1/2
= 0.
5. Monge–Amp` ere equation
det(D2u)
= f.
6. Hamilton–Jacobi equation
ut + H(Du, x) = 0.
7. Scalar conservation law
ut + div F(u) = 0.
8. Inviscid Burgers’ equation
ut + uux = 0.
9. Scalar reaction-diffusion equation
ut Δu = f(u).
10. Porous medium equation
ut
Δ(uγ)
= 0.
11. Nonlinear wave equation
utt Δu + f(u) = 0.
12. Korteweg–deVries (KdV) equation
ut + uux + uxxx = 0.
13. Nonlinear Schr¨ odinger equation
iut + Δu =
f(|u|2)u.
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