2.3. Characteristic Curves

Try these first

1. 1.

   What type of PDE is defined by a discriminant Δ < 0?

   Hint

   Think of someone being steady.

2. 2.

   Which equation represents a parabolic PDE?

   Hint

   Remember diffusion.

3. 3.

   What type of PDE is represented by Δ < 0?

   • Hyperbolic
   • Parabolic
   • Elliptic

   Hint

   Think steady-state.

4. 4.

   True or False: All hyperbolic PDEs require two initial conditions.

   • True
   • False

   Hint

   Remember wave motions.

5. 5.

   Classify the PDE ∂²u/∂x² + 2∂²u/∂y² - ∂u/∂y = 0 and discuss the implications of its classification.

   Hint

   Revisit the discriminant calculation.

6. 6.

   Derive the characteristic curves for the wave equation ∂²u/∂t² - c²∂²u/∂x² = 0.

   Hint

   Think about shifting variables in the equation.