Chem Differential Eq HW Solutions Fall 2011 30

Chem Differential Eq HW Solutions Fall 2011 30 - 30 Chapter...

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Unformatted text preview: 30 Chapter 3 Partial Differential Equations in Rectangular Coordinates 17. We have A(u) = u2, φ(x) = √ x, ⇒ A(u(x(t)), t)) = A(φ(x(0))) = x(0). So the characteristic lines are x = tx(0) + x(0) ⇒ Solving for x(0), we find x(0) = and so u(x, t) = f x(0)(t + 1) − x = 0. x , t+1 x t+1 Now u(x, 0) = f (x) = √ . x. So u(x, t) = x . t+1 ...
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