Practice Characteristic Curves (2.3) - Classification of PDEs (Elliptic, Parabolic, Hyperbolic)

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8 questions

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Exercise
6 questions · about 4 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
What type of PDE is defined by a discriminant Δ < 0?
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Think of someone being steady.
Question 2.
Which equation represents a parabolic PDE?
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Remember diffusion.
3Question 3.
What type of PDE is represented by Δ < 0?
- Hyperbolic
- Parabolic
- Elliptic
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Think steady-state.
4Question 4.
True or False: All hyperbolic PDEs require two initial conditions.
- True
- False
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Remember wave motions.
Question 5.
Classify the PDE ∂²u/∂x² + 2∂²u/∂y² - ∂u/∂y = 0 and discuss the implications of its classification.
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Revisit the discriminant calculation.
Question 6.
Derive the characteristic curves for the wave equation ∂²u/∂t² - c²∂²u/∂x² = 0.
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Think about shifting variables in the equation.

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