Practice Classification Of Second-order Linear Pdes (3.2) - Linear and Non-linear PDEs

Practice: Classification of Second-Order Linear PDEs

Lesson 3.2Linear and Non-linear PDEs

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10 questions

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6 questions · about 4 min · pass mark 70%. Hints available.
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4 questions · about 3 min · pass mark 70%. Hints available.
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6 sample questions

Question 1.
Define a discriminant in your own words.
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Think about how the discriminant relates to the solutions.
Question 2.
What is the condition for a PDE to be hyperbolic?
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Remember the symbol >.
3Question 3.
What is the condition for a PDE to be classified as elliptic?
- D > 0
- D = 0
- D < 0
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Think about Laplace's equation.
4Question 4.
True or False: Hyperbolic PDEs can describe diffusion processes.
- True
- False
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Recall what hyperbolic equations are used for.
Question 5.
Construct a second-order linear PDE that is hyperbolic, provide the coefficients, and calculate the discriminant. Explain why it is hyperbolic.
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Select coefficients carefully to ensure D remains positive.
Question 6.
Given the equation $A \frac{\partial^2 u}{\partial x^2}+B\frac{\partial^2 u}{\partial y^2} + C \frac{\partial^2 u}{\partial y^2} = 0$ , determine conditions on A, B, and C so it becomes an elliptic PDE.
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Manipulate A, B, and C values until D < 0 is achieved.

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