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On the existence of strong solutions to the Cahn-Hilliard-Darcy system with mass source. (English) Zbl 1482.35071

Summary: 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.

MSC:

35D35 Strong solutions to PDEs
35K61 Nonlinear initial, boundary and initial-boundary value problems for nonlinear parabolic equations
35Q35 PDEs in connection with fluid mechanics
76D27 Other free boundary flows; Hele-Shaw flows
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