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arXiv · 2009.13344

On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system with mass source

Andrea Giorgini·Kei Fong Lam·Elisabetta Rocca·Giulio Schimperna
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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 (CHD) 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.

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Andrea Giorgini, Kei Fong Lam, Elisabetta Rocca, Giulio Schimperna. 2020-09-28. On the Existence of Strong Solutions to the Cahn-Hilliard-Darcy system with mass source. https://arxiv.org/abs/2009.13344

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