Exact Controllability of a Semilinear Thermoelastic System with Control Solely in Thermal Equation

Abstract

A result concerning the exact controllability of a semilinear thermoelastic system, in which the control term occurs solely in the thermal equation, is derived under the influence of rotational inertia and Lipschitz nonlinearity, subject to the clamped/Dirichlet boundary conditions. In the proof, we make use of the result given by Avalos (Differential and Integral Equations, 2000; 13(4-6):613-630), which states that the corresponding linear system is exact controllable.

Exact Controllability of Semilinear Thermoelastic Systems with Monotone Nonlinearity

“…Lagnese [4] initially studied the controllability of the linear thermoelastic system. Later, there was a vast amount of literature regarding various types of controllability for the linear and semilinear thermoelastic systems, with the control either as distributed control or thorough the boundary (see [5][6][7][8][9][10][11][12][13][14][15]). Now, consider the two Hilbert spaces H 1 0, and H , defined as…”

“…Avalos [19] proved some controllability results for 2-D nonlinear thermoelastic system in the absence of rotational inertia (that is = 0), and under the influence of the non-Lipschitz von Karman nonlinearity. Tomar and Sukavanam [15] discussed the exact controllability of system (1.6)-(1.9), when the nonlinear functions g 1 and g 2 are Lipschitz continuous without any conditions on their Lipschitz constants.…”

S-Controllability of an Abstract First Order Semilinear Control System

“…Since then controllability of linear and nonlinear deterministic systems represented by ordinary differential equations in finite-dimensional as well as infinite-dimensional spaces have been extensively studied by several authors, see [7,8,12] and references therein.…”