Optimal control of a reflection boundary coefficient in an acoustic wave equation

Abstract

We seek to optimally control a reflection boundary coefficient for an acoustic wave equation. The goal-quantified by an objective functional- is to drive the solution close to a target by adjusting this coefficient, which acts as a control. The problem is solved by finding the optimal control, which minimizes the objective functional. Then the optimal control is used as a an approximation for an inverse “ identification” problem.

Keywords:

• Optimal control
• :wave equation
• Robin boundary condition
• parameter identification

¹University of Tennessee, Mathematics Department, Knoxville, TN 37996-1300

²Oak Ridge National Laboratory, Computer Science and Mathematics Division, Oak Ridge, TN 37831-6364

³Fudan University, Department of Mathematics, Shanghai, 200433 China

¹University of Tennessee, Mathematics Department, Knoxville, TN 37996-1300

²Oak Ridge National Laboratory, Computer Science and Mathematics Division, Oak Ridge, TN 37831-6364

³Fudan University, Department of Mathematics, Shanghai, 200433 China

Notes

¹University of Tennessee, Mathematics Department, Knoxville, TN 37996-1300

²Oak Ridge National Laboratory, Computer Science and Mathematics Division, Oak Ridge, TN 37831-6364

³Fudan University, Department of Mathematics, Shanghai, 200433 China