2.2. Types of PDEs

Try these first

1. 1.

   What is the condition that defines elliptic PDEs?

   Hint

   Think about the discriminant.

2. 2.

   Which PDE is an example of a parabolic equation?

   Hint

   It relates to temperature change.

3. 3.

   What type of PDE is represented by the equation ∂²u/∂x² + ∂²u/∂y² = 0?

   • Elliptic
   • Parabolic
   • Hyperbolic

   Hint

   Consider the discriminant.

4. 4.

   True or False: A hyperbolic PDE has two distinct characteristic curves.

   • True
   • False

   Hint

   Think about wave propagation.

5. 5.

   Given the PDE ∂²u/∂t² - c²∂²u/∂x² = 0, classify it and justify your reasoning.

   Hint

   Evaluate the coefficients to assess the discriminant.

6. 6.

   Transform the parabolic PDE ∂u/∂t = k∂²u/∂x² into its canonical form.

   Hint

   Use variable change methods to simplify the equation.