Question: (a) Find all equilibrium solutions. (b) Prove that all non-constant solutions decay exponentially fast to some equilibrium. What is the decay rate? (c) Is the

(a) Find all equilibrium solutions.
(b) Prove that all non-constant solutions decay exponentially fast to some equilibrium. What is the decay rate?
(c) Is the origin
(i) Stable,
(ii) Asymptotically stable, or
(iii) Unstable?
(d) Prove that, as t †’ ˆž, the solution u(t) converges to the orthogonal projection of its initial vector a = u(0) onto ker K.

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