2015/11/19 by Harald Garcke, Kei Fong Lam, Garcke, Harald +1 · 3 citations
Computer Science · Materials Science · Mathematics · #35K50 #35K57 #35Q92 #92B05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Solidification and crystal growth phenomena #Tissues and Organs (q-bio.TO)
paper · pdf · doi:10.48550/arxiv.1511.06143
openalex publication_date 2015/11/19 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28
We consider a diffuse interface model for tumour growth consisting of a\nCahn--Hilliard equation with source terms coupled to a reaction-diffusion\nequation. The coupled system of partial differential equations models a tumour\ngrowing in the presence of a nutrient species and surrounded by healthy tissue.\nThe model also takes into account transport mechanisms such as chemotaxis and\nactive transport. We establish well-posedness results for the tumour model and\na variant with a quasi-static nutrient. It will turn out that the presence of\nthe source terms in the Cahn--Hilliard equation leads to new difficulties when\none aims to derive a priori estimates. However, we are able to prove continuous\ndependence on initial and boundary data for the chemical potential and for the\norder parameter in strong norms.\n