Boundary Control for Cooperative Elliptic Systems under Conjugation Conditions

Abstract

The existence and uniqueness of the state for 2 × 2 Dirichlet cooperative elliptic systems under conjugation conditions are proved using Lax-Milgram lemma, then the boundary control for these systems is discussed. The set of equations and inequalities that characterizes this boundary control is found by theory of Lions, Sergienko and Deineka. The problem for cooperative Neumann elliptic systems under conjugation conditions is also considered.Finally, the problem for n × n cooperative elliptic systems under conjugation conditions is established.

Optimal control for cooperative systems involving fractional Laplace operators

“…Optimal control for partial differential equations (PDEs) has been widely studied in many fields such as biology, ecology, economics, engineering, and finance [5-10, 18, 22, 24, 25, 30, 34, 37]. These results have been expanded in [12,14,15,29,[31][32][33] to cooperative and noncooperative systems. The fractional optimal control problems are the generalization of standard optimal control problems.…”