Details
| Originalsprache | Englisch |
|---|---|
| Titel des Sammelwerks | Modelling, Simulation and Software Concepts for Scientific-Technological Problems |
| Seiten | 237-250 |
| Seitenumfang | 14 |
| Publikationsstatus | Veröffentlicht - 2011 |
Publikationsreihe
| Name | Lecture Notes in Applied and Computational Mechanics |
|---|---|
| Band | 57 |
| ISSN (Print) | 1613-7736 |
Abstract
A model describing the growth of necrotic tumors in different regimes of vascularisation is studied. The tumor consists of a necrotic core of death cells and a surrounding shell which contains life-proliferating cells. The blood supply provides the nonnecrotic region with nutrients and no inhibitor chemical species are present. The corresponding mathematical formulation is a moving boundary problem since both boundaries delimiting the nonnecrotic shell are allowed to evolve in time. We determine all radially symmetric stationary solutions and reduce the moving boundary problem into a nonlinear evolution equation for the functions parameterising the boundaries of the shell. Parabolic theory provides a suitable context for proving local well-posedness of the problem for small initial data.
ASJC Scopus Sachgebiete
- Ingenieurwesen (insg.)
- Maschinenbau
- Informatik (insg.)
- Theoretische Informatik und Mathematik
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Modelling, Simulation and Software Concepts for Scientific-Technological Problems. 2011. S. 237-250 (Lecture Notes in Applied and Computational Mechanics; Band 57).
Publikation: Beitrag in Buch/Bericht/Sammelwerk/Konferenzband › Beitrag in Buch/Sammelwerk › Forschung › Peer-Review
}
TY - CHAP
T1 - Analysis of a mathematical model describing necrotic tumor growth
AU - Escher, Joachim
AU - Matioc, Anca Voichita
AU - Matioc, Bogdan-Vasile
PY - 2011
Y1 - 2011
N2 - A model describing the growth of necrotic tumors in different regimes of vascularisation is studied. The tumor consists of a necrotic core of death cells and a surrounding shell which contains life-proliferating cells. The blood supply provides the nonnecrotic region with nutrients and no inhibitor chemical species are present. The corresponding mathematical formulation is a moving boundary problem since both boundaries delimiting the nonnecrotic shell are allowed to evolve in time. We determine all radially symmetric stationary solutions and reduce the moving boundary problem into a nonlinear evolution equation for the functions parameterising the boundaries of the shell. Parabolic theory provides a suitable context for proving local well-posedness of the problem for small initial data.
AB - A model describing the growth of necrotic tumors in different regimes of vascularisation is studied. The tumor consists of a necrotic core of death cells and a surrounding shell which contains life-proliferating cells. The blood supply provides the nonnecrotic region with nutrients and no inhibitor chemical species are present. The corresponding mathematical formulation is a moving boundary problem since both boundaries delimiting the nonnecrotic shell are allowed to evolve in time. We determine all radially symmetric stationary solutions and reduce the moving boundary problem into a nonlinear evolution equation for the functions parameterising the boundaries of the shell. Parabolic theory provides a suitable context for proving local well-posedness of the problem for small initial data.
UR - http://www.scopus.com/inward/record.url?scp=79955861311&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-20490-6-10
DO - 10.1007/978-3-642-20490-6-10
M3 - Contribution to book/anthology
AN - SCOPUS:79955861311
SN - 9783642204890
T3 - Lecture Notes in Applied and Computational Mechanics
SP - 237
EP - 250
BT - Modelling, Simulation and Software Concepts for Scientific-Technological Problems
ER -