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## Regularization of a chemoattraction model with consumption

### André Luiz Corrêa Vianna Filho

#### Federal University of Paraná (UFPR), Brazil   -   This email address is being protected from spambots. You need JavaScript enabled to view it. document.getElementById('cloak7362b3409840568de62d0fa242cd2494').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addy7362b3409840568de62d0fa242cd2494 = 'v&#105;&#97;nn&#97;f&#105;lh&#111;&#97;ndr&#101;' + '&#64;'; addy7362b3409840568de62d0fa242cd2494 = addy7362b3409840568de62d0fa242cd2494 + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m'; var addy_text7362b3409840568de62d0fa242cd2494 = 'v&#105;&#97;nn&#97;f&#105;lh&#111;&#97;ndr&#101;' + '&#64;' + 'gm&#97;&#105;l' + '&#46;' + 'c&#111;m';document.getElementById('cloak7362b3409840568de62d0fa242cd2494').innerHTML += '<a ' + path + '\'' + prefix + ':' + addy7362b3409840568de62d0fa242cd2494 + '\'>'+addy_text7362b3409840568de62d0fa242cd2494+'<\/a>';

Chemotaxis is the movement of cells in response to the concentration gradient of a chemical substance. It plays an important role in wound healing, migration of immune cells, migration of bacteria and other relevant situations which make of chemotaxis a matter of very practical interest. Cells can be attracted (chemoattraction) or repeled (chemorepulsion) by the by the greater concentration of this chemical substance. In this work we investigate a chemoattraction model, which we call the original model, with consumption, in non-smooth bounded domains of $R^N$ ($N = 1, 2, 3$). The non-linear term related to the chemotaxis phenomenon introduces many difficulties to the analysis of the original model, mainly for its numerical simulation. In order to overcome these difficulties, we propose and analyze a regularized model, establishing results on existence, uniqueness, regularity’s properties and convergence of its solutions towards the original model.

Joint work with Francisco Guillén-González (Universidad de Sevilla, Spain) and Pedro Danizete Damázio (Federal University of Paraná, Brazil).