2.1. Classification Based on Discriminant

Try these first

1. 1.

   What is the condition for an elliptic PDE?

   Hint

   Think about what the discriminant represents.

2. 2.

   Which type of PDE corresponds to Δ = 0?

   Hint

   Remember the heat equation!

3. 3.

   What is the condition for characterizing an elliptic PDE?

   • Δ < 0
   • Δ = 0
   • Δ > 0

   Hint

   Think about steady-state processes.

4. 4.

   True or False: Parabolic PDEs require two initial conditions.

   • True
   • False

   Hint

   Recall the heat equation.

5. 5.

   Given the PDE: 3∂²u/∂x² + 4∂²u/∂y² − 6∂u/∂x + 2u = 0, classify it and provide justification.

   Hint

   Focus on identifying A, B, C first.

6. 6.

   Classify the PDE: ∂²u/∂x² - ∂²u/∂y² = 0, and explain the classification.

   Hint

   Make sure to compute the discriminant.