Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with chemotaxis
Matthias Ebenbeck,Harald Garcke +1 more
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In this paper, a new Cahn-Hilliard-Brinkman model for tumour growth allowing for chemotaxis is introduced and mathematically analyzed, and the existence of global-in-time weak solutions is shown in a very general setting.About:
This article is published in Journal of Differential Equations.The article was published on 2019-04-15 and is currently open access. It has received 65 citations till now. The article focuses on the topics: Context (language use).read more
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On a phase field model of Cahn–Hilliard type for tumour growth with mechanical effects
TL;DR: In this article, the authors studied a macroscopic mechanical model for phase field tumour growth in which cell-cell adhesion effects are taken into account with the help of a Ginzburg-Landau type energy.
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Optimal control theory and advanced optimality conditions for a diffuse interface model of tumor growth
Matthias Ebenbeck,Patrik Knopf +1 more
TL;DR: In this paper, a distributed optimal control problem for a diffuse interface model for tumor growth is investigated, where the control represents a medication by cytotoxic drugs and enters the phase field equation.
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Optimal medication for tumors modeled by a Cahn–Hilliard–Brinkman equation
Matthias Ebenbeck,Patrik Knopf +1 more
TL;DR: In this paper, a distributed optimal control problem for a diffuse interface model for tumor growth is studied, where the control acts as a medication by cytotoxic drugs and enters the phase field equation.
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On the unsteady Darcy–Forchheimer–Brinkman equation in local and nonlocal tumor growth models
TL;DR: A mathematical analysis of local and non-local phase-field models of tumor growth is presented in this paper that includes time-dependent Darcy-Forchheimer-Brinkman models of convective velocity fields and models of nonlocal phase fields.
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Vanishing parameter for an optimal control problem modeling tumor growth
TL;DR: In this article, a distributed optimal control problem for a phase field system which physical context is that of tumor growth is discussed, where two small and positive parameters are introduced in previous contributions as relaxation terms.
References
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Theory of Dynamic Critical Phenomena
TL;DR: The renormalization group theory has been applied to a variety of dynamic critical phenomena, such as the phase separation of a symmetric binary fluid as mentioned in this paper, and it has been shown that it can explain available experimental data at the critical point of pure fluids, and binary mixtures, and at many magnetic phase transitions.
Journal ArticleDOI
Compact sets in the spaceL p (O,T; B)
TL;DR: In this paper, a characterization of compact sets in Lp (0, T; B) is given, where 1⩽P⩾∞ and B is a Banach space.
Journal ArticleDOI
A calculation of the viscous force exerted by a flowing fluid on a dense swarm of particles
TL;DR: In this paper, the viscous force exerted by a flowing fluid on a dense swarm of particles is described by a modification of Darcy's equation, which was necessary in order to obtain consistent boundary conditions.
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Numerical Methods for Nonlinear Variational Problems
Roland Glowinski,J. T. Oden +1 more
Book
An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Steady-State Problems
TL;DR: Steady-State Solutions of the Navier-Stokes Equations: Statement of the Problem and Open Questions as mentioned in this paper The Navier Stokes Equation (NSE) is a stable state solution of the NSE.