Identification of the source for full parabolic equations

GUILLERMO FEDERICO UMBRICHT

Buenos Aires

Congreso; Congreso Matemático de las Américas 2021 (MCA); 2021

Facultad de Ciencias Exactas y Naturales, Universidad Nacional de Buenos Aires

In this work, we consider the problem of identifying the time independentsource for full parabolic equations in Rn from noisy data. This is an ill-posedproblem in the sense of Hadamard. To compensate the factor that causes the instability,a family of parametric regularization operators is introduced, where the ruleto select the value of the regularization parameter is included. This rule, known asregularization parameter choice rule, depends on the data noise level and the degreeof smoothness that it is assumed for the source. The proof for the stability andconvergence of the regularization criteria is presented and a Holder type bound isobtained for the estimation error. Numerical examples are included to illustrate theeffectiveness of this regularization approach.