On a construction of Green's functions for a system with distributed parameters (Q2739959)

Let the system state \(y(x,t)\) satisfy in the domain \(\{(x,t):0\leq x_{i}<\infty\), \(i=1,\ldots,n\), \(0\leq t<\infty\}\) the equation \(L_1(\partial x,\partial t)y(x,t)=L_2(\partial x,\partial t)u(x,t)\), \(y(x,0)=0\), where \(L_{i}\) are given differential operators. The author proposes a method of constructing the Green function and partial solutions for the considered system. As applications of the proposed method the classical equations of mathematical physics and problems of electrodynamics are considered.