Approximate controllability of second-order semilinear evolution systems with finite delay
In the paper, the authors study second-order semilinear evolution equations with finite time delay. First, via proving the existence and uniqueness of mild solutions of the corresponding linear system the authors construct the fundamental solution and discuss regularity properties for it. After that, they present the mild solution of semilinear system via the fundamental solution of linear system using Laplace transform techniques. Then, the authors study the approximate controllability of the given system by employing the resolvent condition and obtain some sufficient conditions for approximate controllability. In the final part of the paper, the general results are illustrarated with an example.
scientific article; zbMATH DE number 7382611
scientific article