Nonlinear Inverse Problems and Singular Integral Equations

点击翻译按钮获取中文摘要

Several nonlinear inverse problems in mathematical sciences are discussed : a friction coefficient identification problem, a nonlinearity identification problem in nonlinear oscillations, a time-dependent thermal conductivity identification problem, inverse bifurcation problem in mathematical ecology (nonlinear reaction kinetics identification problem in a diffusional model of population dynamics from the relation between growth rates and certain central densities of population distributions). A certain class of singular integral equations plays a principal role in our mathematical analysis of the inverse problems ; some existence results of the solutions to the integral equations are established and applied to the inverse problems.