Parameter identification by solution of inverse problem referred to mathematical models of continuum physics (Q1813885)

This paper deals with mathematical models which describe the time-space evolution of the state variables of systems in continuum physics, say \(u=u(t,x)\), by means of partial differential equations involving an unknown function of the space, say \(\alpha=\alpha(x)\). The mathematical problem consists in computing \(\alpha=\alpha(x)\) if at a fixed time \(t=t^*\) the function \(u=u(t^*,x)\) is given as a solution of some initial-boundary value problem. The problem is solved by the so called Bellman-Adomian method which consists in discretizing the space variable in order to transform the initial-boundary value problem described by partial differential equations into an initial value problem described by a system of ordinary differential equations obtained by Bellman's differential quadrature method. Such a system is then solved by Adomian's decomposition method which provides an approximated analytic solution suitable to solve the inverse problem.