An uncoupling procedure for a class of coupled linear partial differential equations

Source abstract

Abstract A Fredholm operator exists which maps the solutions of a system of linear partial differential equations of the form ∂ u /∂ t = DLu + Au coupled by a matrix A onto those solutions of a similar system coupled by a matrix B which have the same initial values. The kernels of this operator satisfy a hyperbolic system of equations. Since these equations are independent of the linear partial differential operator L , the same operator serves as a mapping for a large class of equations. If B is chosen diagonal, the solutions of a coupled system with matrix A may be obtained from the uncoupled system with matrix B .