Wave equation $u_{tt} = u_{xx}$
Terms
| Term | This example | Why |
|---|---|---|
| hyperbolic pde | ✓ | The wave equation is hyperbolic because $u_{tt} - u_{xx} = 0$ has $A = 1$ and $C = -1$, so $B^2 - AC = 1 > 0$. |
| elliptic pde | ✗ | |
| parabolic pde | ✗ |
| Term | This example | Why |
|---|---|---|
| hyperbolic pde | ✓ | The wave equation is hyperbolic because $u_{tt} - u_{xx} = 0$ has $A = 1$ and $C = -1$, so $B^2 - AC = 1 > 0$. |
| elliptic pde | ✗ | |
| parabolic pde | ✗ |