Consider the equation where q(y) - 0, 1. y < 1 |y| 1. y >...

 

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Consider the equation where q(y) - 0, 1. y < −1 |y| ≤ 1. y > 1 Uxx + 2Uxy + (1 − q (y))Uyy ² 0 i) Find the domains where the equation is hyperbolic, parabolic, and elliptic. ii) For each of the above three domains, find the corresponding canonical transformation and the canonical form. Consider the equation where q(y) - 0, 1. y < −1 |y| ≤ 1. y > 1 Uxx + 2Uxy + (1 − q (y))Uyy ² 0 i) Find the domains where the equation is hyperbolic, parabolic, and elliptic. ii) For each of the above three domains, find the corresponding canonical transformation and the canonical form.

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