From short-range repulsion to Hele-Shaw problem in a model of tumor growth
نویسندگان
چکیده
منابع مشابه
The Hele-Shaw asymptotics for mechanical models of tumor growth
Models of tumor growth, now commonly used, present several levels of complexity, both in terms of the biomedical ingredients and the mathematical description. The simplest ones contain competition for space using purely fluid mechanical concepts. Another possible ingredient is the supply of nutrients through vasculature. The models can describe the tissue either at the level of cell densities, ...
متن کاملTraveling wave solution of the Hele-Shaw model of tumor growth with nutrient
Several mathematical models of tumor growth are now commonly used to explain medical observations and predict cancer evolution based on images. These models incorporate mechanical laws for tissue compression combined with rules for nutrients availability which can differ depending on the situation under consideration, in vivo or in vitro. Numerical solutions exhibit, as expected from medical ob...
متن کاملAsymptotic Convergence of the Stefan Problem to Hele-shaw
We discuss the asymptotic behaviour of weak solutions to the Hele-Shaw and one-phase Stefan problems in exterior domains. We prove that, if the space dimension is greater than one, the asymptotic behaviour is given in both cases by the solution of the Dirichlet exterior problem for the Laplacian in the interior of the positivity set and by a singular, radial and self-similar solution of the Hel...
متن کاملGlobal Solutions for Small Data to the Hele-shaw Problem
We analyze an equation governing the motion of an interface between two fluids in a pressure field. In two dimensions, the interface is described by a conformal mapping which is analytic in the exterior of the unit disc. This mapping obeys a nonlocal nonlinear equation. When there is no pumping at infinity, there is conservation of area and contraction of the length of the interface. We prove g...
متن کاملfrom linguistics to literature: a linguistic approach to the study of linguistic deviations in the turkish divan of shahriar
chapter i provides an overview of structural linguistics and touches upon the saussurean dichotomies with the final goal of exploring their relevance to the stylistic studies of literature. to provide evidence for the singificance of the study, chapter ii deals with the controversial issue of linguistics and literature, and presents opposing views which, at the same time, have been central to t...
15 صفحه اولذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Mathematical Biology
سال: 2017
ISSN: 0303-6812,1432-1416
DOI: 10.1007/s00285-017-1143-4