Solving the inverse problem of determining an unknown control parameter in a semilinear parabolic equation

Abstract

The inverse problem of identifying an unknown source control param- <br />eter in a semilinear parabolic equation under an integral overdetermina- <br />tion condition is considered. The series pattern solution of the proposed <br />problem is obtained by using the weighted homotopy analysis method <br />(WHAM). A description of the method for solving the problem and nding <br />the unknown parameter is derived. Finally, two numerical examples are <br />investigated to illustrate this method.