@article{2e24ff5c726449b2ad97c79939cf65a6,
title = "On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy System with Mass Source",
abstract = "We study a diffuse interface model describing the evolution of the flow of a binary fluid in a Hele-Shaw cell. The model consists of a Cahn--Hilliard--Darcy type system with transport and mass source. A relevant physical application is related to tumor growth dynamics, which in particular justifies the occurrence of a mass inflow. We study the initial-boundary value problem for this model and prove global existence and uniqueness of strong solutions in two space dimensions as well as local existence in three space dimensions.",
keywords = "Cahn-Hilliard-Darcy system, logarithmic potentials, nonlinear evolutionary system, strong solutions, well-posedness",
author = "Andrea Giorgini and Lam, {Kei Fong} and Elisabetta Rocca and Giulio Schimperna",
note = "Funding Information: The work of the authors was supported by the Italian Ministry of Education, Uni-versity and Research (MIUR): Dipartimenti di Eccellenza Program (2018-2022); the Departmentof Mathematics ``F. Casorati,{"}{"} University of Pavia; and the GNAMPA-INdAM project ``Analisimatematica di modelli a interfaccia diffusa per fluidi complessi,{"}{"} and by the project FondazioneCariplo-Regione Lombardia MEGAsTAR ``Matematica d'Eccellenza in biologia ed ingegneria comeacceleratore di una nuova strateGia per l'ATtRattivit\`a dell'ateneo pavese.{"}{"} The work of the fourthauthor was also supported by MIUR-PRIN grant 2015PA5MP7, ``Calculus of Variations.{"}{"} The workof the first, third, and fourth authors was also supported by the GNAMPA (Gruppo Nazionale perl'Analisi Matematica, la Probabilit\`a e le loro Applicazioni) of INdAM (Istituto Nazionale di AltaMatematica). The work of the second author was also supported by the Research Grants Council ofthe Hong Kong Special Administrative Region, project HKBU 14302319. Publisher Copyright: {\textcopyright} 2022 Society for Industrial and Applied Mathematics",
year = "2022",
month = jan,
doi = "10.1137/20M1376443",
language = "English",
volume = "54",
pages = "737--767",
journal = "SIAM Journal on Mathematical Analysis",
issn = "0036-1410",
publisher = "Society for Industrial and Applied Mathematics (SIAM)",
number = "1",
}