Problem of innovation diffusion: qualitative investigation and algorithmic aspect.
The authors consider the following optimal control problem: \[ J(u)=\int_0^Te^{-\nu_2 t}(\ln x +g_2\ln(L-u))\, dt\to \max, \] \[ \dot x=u(x+g_1e^{\nu_1 t}),\quad x(0)=x_0,\, 0\leq u< L, \] arising in an economic dynamical problem and modeling innovation with diffusion. They suggest algorithms for the solution of this problem and also methods for constructing the attainability domain. Results of numerical experiments carried out in MAPLE are also presented.
scientific article; zbMATH DE number 2099451