Constructive solution of strongly coupled continuous hyperbolic mixed problems. (Q1417629)

Using a matrix separation of variables method, the authors construct exact series solutions of mixed problems for strongly coupled hyperbolic partial differential systems of the form \[ Au_{xx}(x,t) = u_{tt}, \quad 0<x<1,\;t > 0, \] \[ u(0,t) + B_1 u_x(0,t)= 0, \quad t > 0, \] \[ A_2 u(x,t) + B_2 u_x(x,t)= 0, \quad t >0, \] \[ u(x,0)=f(x), \quad u_t(x,0) = g(x),\;0\leq x \leq 1. \] Here, \(A, B_1,A_2,B_2\) are \(m\times m\) complex matrices of \(\mathbb{C}^{m\times m}\) and the unknown \(u\), the data \(f\) and \(g\) are \(\mathbb{C}^{m}\) valued functions.