Mathematics

Dominguez

10 February, 04:45

Find the solution of the initial value problem ˙~x = F~ (~x) with ~x (0) = ~x0 for F~ (~x) = - µx1 - x2 + x 2 1, ~x = x1 x2, ~x0 = a b for arbitrarily chosen (a, b, µ) ∈ R 3. Is the solution ~u (t; a, b, µ) a continuous function of all variables (t, a, b, µ) ∈ R 4? Give an interval t ∈ [-a, a] and an open neighbourhood (a, b, µ) ∈ U ⊂ R 3 such that ~u ∈ C ([-a, a] * U, R 3).