Ebenbeck, Matthias ; Garcke, Harald ; Nürnberg, Robert
Alternative Links zum Volltext:DOIVerlag
| Dokumentenart: | Artikel |
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| Titel eines Journals oder einer Zeitschrift: | Discrete and Continuous Dynamical Systems - Series S |
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| Verlag: | AMER INST MATHEMATICAL SCIENCES-AIMS |
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| Ort der Veröffentlichung: | SPRINGFIELD |
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| Band: | 14 |
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| Nummer des Zeitschriftenheftes oder des Kapitels: | 11 |
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| Seitenbereich: | S. 3989 |
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| Datum: | 2021 |
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| Institutionen: | Mathematik > Prof. Dr. Harald Garcke |
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| Identifikationsnummer: | | Wert | Typ |
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| 10.3934/dcdss.2021034 | DOI |
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| Stichwörter / Keywords: | FREE-BOUNDARY PROBLEM; PHASE FIELD MODEL; FINITE-ELEMENT APPROXIMATION; DARCY SYSTEM; NONLINEAR SIMULATION; MIXTURE MODEL; EQUATION; FORCHHEIMER; STABILITY; ALGORITHM; Cahn-Hilliard equation; phase field model; Brinkman model; existence; singular limit; finite elements; Tumour growth |
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| Dewey-Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik > 510 Mathematik
600 Technik, Medizin, angewandte Wissenschaften > 610 Medizin |
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| Status: | Veröffentlicht |
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| Begutachtet: | Ja, diese Version wurde begutachtet |
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| An der Universität Regensburg entstanden: | Ja |
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| Dokumenten-ID: | 55780 |
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Zusammenfassung
A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a con-vective Cahn-Hilliard equation for the evolution of the tumour to a reaction-diffusion-advection equation for a nutrient and to a Brinkman-Stokes type law for the fluid velocity. The model is derived from basic thermodynamical principles, sharp interface ...
Zusammenfassung
A phase field model for tumour growth is introduced that is based on a Brinkman law for convective velocity fields. The model couples a con-vective Cahn-Hilliard equation for the evolution of the tumour to a reaction-diffusion-advection equation for a nutrient and to a Brinkman-Stokes type law for the fluid velocity. The model is derived from basic thermodynamical principles, sharp interface limits are derived by matched asymptotics and an existence theory is presented for the case of a mobility which degenerates in one phase leading to a degenerate parabolic equation of fourth order. Finally numerical results describe qualitative features of the solutions and illustrate instabilities in certain situations.
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