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homework12

# homework12 - Math 21a Homework 12 Extra Problems Spring...

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Unformatted text preview: Math 21a Homework 12: Extra Problems Spring, 2009 1 The partial differential equation u t = au x is known as the transport equation (or sometimes the advection equation ). In this problem we’ll find solutions u ( x,t ) to this equation. In particular, we’ll include an initial condition and solve the initial value problem (IVP) ( * )    ∂u ∂t = a ∂u ∂x u ( x, 0) = f ( x ) . (a) Here is a graph of u = f ( x ) (an example initial condition for the IVP): ................................................................................................................................................................................................................................................................................................................................ . . . . . . . . . . . . . x . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
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