Suppose that u(t) satisfies the gradient flow system (9.21). (a) Prove that d/dt q(u) = ||ku||2. (b)
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(a) Prove that d/dt q(u) = ||ku||2.
(b) Explain why if u(t) is any nonconstant solution to the gradient flow, then q(u(t)) is a strictly decreasing function of t, thus quantifying how fast a gradient flow decreases energy.
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a When qu 12 u T Ku then b Since Ku 0 when u ker K ddt qu Ku 2 0 an...View the full answer
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