3.3.1. Parabolic PDEs

Try these first

1. 1.

   What is the discriminant condition for parabolic PDEs?

   Hint

   Remember how discriminants classify PDE types.

2. 2.

   What does the heat equation model?

   Hint

   Think about heat transfer in objects.

3. 3.

   What is the discriminant for parabolic PDEs?

   • D > 0
   • D = 0
   • D < 0

   Hint

   Recall how discriminants classify the types of PDEs.

4. 4.

   The heat equation is an example of:

   • True
   • False

   Hint

   Consider how we have defined the heat equation.

5. 5.

   Given the initial temperature distribution along a rod is T(x,0) = sin(πx) for 0 ≤ x ≤ 1, derive the temperature distribution at time t > 0 using the heat equation.

   Hint

   Consider using Fourier series for periodic initial conditions.

6. 6.

   A wire of length L has an initial temperature distribution T(x,0) = T0 at x = 0 and T1 at x = L. How would you set this up as an initial value problem for a parabolic PDE?

   Hint

   Think about how to express constant boundary conditions in terms of heat flow.