English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

This paper provides a unified mathematical analysis of a family of non-localdiffuse interface models for tumor growth describing evolutions driven bylong-range interactions. These integro-partial differential equations modelcell-to-cell adhesion by a non-local term and may be seen as non-local variantsof the corresponding local model proposed by H. Garcke et al. (2016). The modelin consideration couples a non-local Cahn-Hilliard equation for the tumor phasevariable with a reaction-diffusion equation for the nutrient concentration, andtakes into account also significant mechanisms such as chemotaxis and activetransport. The system depends on two relaxation parameters: a viscositycoefficient and parabolic-regularization coefficient on the chemical potential.The first part of the paper is devoted to the analysis of the system with bothregularizations. Here, a rich spectrum of results is presented. Weakwell-posedness is first addressed, also including singular potentials. Then,under suitable conditions, existence of strong solutions enjoying theseparation property is proved. This allows also to obtain a refined stabilityestimate with respect to the data, including both chemotaxis and activetransport. The second part of the paper is devoted to the study of theasymptotic behavior of the system as the relaxation parameters vanish. Theasymptotics are analyzed when the parameters approach zero both separately andjointly, and exact error estimates are obtained. As a by-product,well-posedness of the corresponding limit systems is established.

On a class of non-local phase-field models for tumor growth with possibly singular potentials, chemotaxis, and active transport