Unique solvability for an inverse problem of a nonlinear parabolic PDE with nonlocal integral overdetermination condition

Abstract

In this work, the solvability for an inverse problem of a nonlinear parabolic equation with nonlocal integral overdetermination supplementary condition is examined. The proof of the existence and uniqueness of the solution of the inverse nonlinear parabolic problem upon the data is established by using the fixed-point technique. In addition, the inverse problem is investigated by using the cubic B-spline collocation technique together with the Tikhonov regularization. The resulting nonlinear system of parabolic equation is approximated using the MATLAB subroutine lsqnonlin. The obtained results demonstrate the accuracy and efficiency of the technique, and the stability of the approximate solutions even in the existence of noisy data. The stability analysis is also conducted for the discretized system of the direct problem.

Keywords

• nonlinear parabolic equation
• collocation technique
• tikhonov regularization
• nonlinear optimization
• 65mxx
• 35r30
• 47h10