We have the equations

$$ rho (x) frac { partial ^ 2u} { partial ^ 2} (t, x) = div (A (x) degrees u + B (x) grad frac { partial u} { partial t}) (t, x) -div ( gamma (x) v (t, x)) $$

$$ beta (x) frac { partial v} { partial t} (t, x) = div (C (x) degree v) (t, x) – gamma (x) .grad frac { partial u} { partial t} (t, x) $$

This leads to an operator

$$ A = begin {pmatrix} 0 &, I &, 0 \ frac {1} { rho (x)} div A (x) grad &, frac {1} { rho (x)} div B (x) grad &, frac {-1} { rho (x)} div gamma (x) \ 0 &, frac {-1} { beta (x)} gamma (x) grad &, frac {1} { beta (x)} div C (x) grad end {pmatrix} $$

Now A continues to work $ (u_1, u_2, u_3) ^ T $How do I find the associated form of A?

Help Thanks