Averaging for ordinary differential equations perturbed by a small parameter

Approximate Optimal Control for a Parabolic System with Perturbations in the Coefficients on the Half-Axis

“…The work [8] is devoted to using an asymptotic method for studying the Cauchy problem for a 1D Euler-Poisson system, which represents a physically relevant hydrodynamic model but also a challenging case for a bipolar semiconductor device by considering two different pressure functions. In [9], the averaging results for ordinary differential equations perturbed by a small parameter are proved. Here, authors assume only that the right-hand sides of the equations are bounded by some locally Lebesgue integrable functions with the property that their indefinite integrals satisfy a Lipschitz-type condition.…”