An application of semigroup method in a parabolic equation with mixed boundary conditions

Abstract

This article presents analysis of the inverse coefficient problems of identifying the unknown diffusion coefficient in a quasi-linear parabolic equation, with mixed boundary conditions. By using semigroup theory we examined the distinguishability of the input-output mappings. If the null space of the semigroups consist of zero function, then we concluded that the input-output mappings have the distinguishability property. The values of k(u(0,0)) and k(u(1,t)) can be determined by making use of measured output data. Hence we redefine the new set of admissible coefficients. The semigroup representations of the input-output mappings are obtained in integral form. Moreover the input-output mappings are obtained explicitly in integral form. © 2008 American Institute of Physics.