Practice Examples For Practice (2.5) - Classification of PDEs (Elliptic, Parabolic, Hyperbolic)

Practice: Examples for Practice

Lesson 2.5Classification of PDEs (Elliptic, Parabolic, Hyperbolic)

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8 questions

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3 cards from this section. Quick, good the night before a test.
Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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2 questions · about 1 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Classify the PDE ∂²u/∂x² + ∂²u/∂y² = 0.
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Check the coefficients and calculate the discriminant.
Question 2.
What type of PDE is ∂u/∂t - ∂²u/∂x² = 0?
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Identify the coefficients and find the discriminant.
3Question 3.
What is the classification type for a PDE with discriminant Δ < 0?
- Elliptic
- Parabolic
- Hyperbolic
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Think about the conditions of steady-state systems.
4Question 4.
True or False: A parabolic PDE has two distinct characteristic lines.
- True
- False
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Consider what a parabolic shape looks like.
Question 5.
For the PDE ∂²u/∂t² - 9∂²u/∂x² = 0, classify, interpret its physical significance, and solve for the general solution.
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Focus on separating variables and considering initial conditions.
Question 6.
Classify and analyze the PDE ∂²u/∂x² + 4∂²u/∂y² = 0, ensuring you work out boundary conditions.
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Think about constant solutions in a bounded domain.

4 more questions in this section. Enroll free to practise them all.