Strong periodic solutions for a class of abstract evolution equations.
The authors deal with the existence, uniqueness and stability of strong periodic solutions to a class of abstract evolution equations of the form \[ \frac d{dt}u + Lu + B(u,u)+ Ru = f \] in a separable Hilbert space \(H\). Here, \(L\) is a selfadjoint strictly positive operator on \(H\), \(B\) a bilinear form on \(H\times H\), \(R\) a linear operator and \(f\) a periodic function. The main tool for proving the results is based on some estimates on approximation solutions. An application of the existence theorem to the system of equations of magneto-micropolar fluids and the Navier-Stokes system is given, too.
scientific article; zbMATH DE number 1963678