Relaxation of nonlocal m-dissipative differential inclusions

Abstract

We show here that the set of the integral solutions of a nonlocal differential inclusion is dense in the set of the solution set of the corresponding relaxed differential inclusion. We further define a notion of limit solution and show that the set of limit solutions is closed and is the closure of the set of integral solutions. An illustrative example is provided.

Keywords

• m-dissipative functional evolution inclusions
• nonlocal initial conditions
• primary 34b15
• secondary 34a60, 35r70