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### Session S08 - Inverse Problems and Applications

Wednesday, July 14, 18:20 ~ 18:50 UTC-3

## Identification of the source for full parabolic equations

### Guillermo Federico Umbricht

#### Universidad Nacional de San Martín / Universidad Nacional de General Sarmiento, Argentina   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloakc61740d8c6fd4510c06f4868885ab061').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyc61740d8c6fd4510c06f4868885ab061 = 'g&#117;&#105;ll&#101;&#117;ngs' + '&#64;'; addyc61740d8c6fd4510c06f4868885ab061 = addyc61740d8c6fd4510c06f4868885ab061 + 'y&#97;h&#111;&#111;' + '&#46;' + 'c&#111;m' + '&#46;' + '&#97;r'; var addy_textc61740d8c6fd4510c06f4868885ab061 = 'g&#117;&#105;ll&#101;&#117;ngs' + '&#64;' + 'y&#97;h&#111;&#111;' + '&#46;' + 'c&#111;m' + '&#46;' + '&#97;r';document.getElementById('cloakc61740d8c6fd4510c06f4868885ab061').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyc61740d8c6fd4510c06f4868885ab061 + '\'>'+addy_textc61740d8c6fd4510c06f4868885ab061+'<\/a>';

In this work, we consider the problem of identifying the time independent source for full parabolic equations in $\mathbb{R}^n$ from noisy data. This is an ill-posed problem in the sense of Hadamard. To compensate the factor that causes the instability, a family of parametric regularization operators is introduced, where the rule to select the value of the regularization parameter is included. This rule, known as regularization parameter choice rule, depends on the data noise level and the degree of smoothness that it is assumed for the source. The proof for the stability and convergence of the regularization criteria is presented and a Hölder type bound is obtained for the estimation error. Numerical examples are included to illustrate the effectiveness of this regularization approach.

Important: The presentation will be in English but the talk will be in Spanish.