Existence and uniqueness for a nonlinear inverse reaction-diffusion problem with a nonlinear source in higher dimensions

This paper analyzes the existence and the uniqueness problem for an n-dimensional nonlinear inverse reaction-diffusion problem with a nonlinear source. A transformation is used to obtain a new inverse coefficient problem. Then, a parabolic differential operator L is defined to establish the relation between the solution of L=0 and the new inverse problem. Following this, it is shown that the inverse problem has at least one solution in the class of admissible coefficients. Furthermore, it is proved that this solution is the unique solution of the undertaken inverse problem. A numerical example is given to illustrate ill-posedness of the inverse problem. Copyright (c) 2013 John Wiley & Sons, Ltd.