A Hele-Shaw Limit Without Monotonicity
نویسندگان
چکیده
We study the incompressible limit of porous medium equation with a right hand side representing either source or sink term, and an injection boundary condition. This model can be seen as simplified description non-monotone motions in tumor growth crowd motion, generalizing congestion-only studied recent literature (\cite{AKY}, \cite{PQV}, \cite{KP}, \cite{MPQ}). characterize density, which solves free problem Hele-Shaw type terms pressure. The novel feature our result lies characterization pressure, obstacle at each time evolution
منابع مشابه
Imperfect Hele - Shaw cells
2014 The covering surfaces of a Hele-Shaw cell may be roughened mechanically, or modified by random chemical patches which change the wetting properties. We discuss first the quasi-static injection of a single fluid (with a finite contact angle 03B8e) in an imperfect cell. The shape of the injected region depends critically on a dimensionless number i (ratio of the boundary energy 03C4 over the...
متن کاملA kinetic formulation of Hele-Shaw flow
In this note we consider a fourth order degenerate parabolic equation modeling the evolution of the interface of a spreading droplet. The equation is approximated trough a collisional kinetic equation. This permits to derive numerical approximations that preserves positivity of the solution and the main relevant physical properties. A Monte Carlo application is also shown. Formulation cinétique...
متن کاملA Multiphase Hele-shaw Flow with Solidification
The one-phase Hele-Shaw flow has a long history and has been extensively studied from several point of views ranging from the fluid dynamical beginnings to complex analysis and integrable systems, see [5]. We prove existence, using the implicit function theorem, of a solution Wε in the Bochner space L2(0, T ;H1 0 (Ω;Rm)) to a non-local in time semi-linear system of coupled PDEs of second order ...
متن کاملSingularity Formation in Hele-Shaw Bubbles
We provide numerical and analytic evidence for the formation of a singu-larity driven only by surface tension in the mathematical model describing a two-dimensional Hele-Shaw cell with no air injection. Constantin and Pugh have proved that no such singularity is possible if the initial shape is close to a circle; thus we show that their result is not true in general. Our evidence takes the form...
متن کاملSynchronization between two hele-shaw cells.
Complete synchronization between two Hele-Shaw cells is examined. The two dynamical systems are chaotic in time and spatially extended in two dimensions. It is shown that a large number of connectors are needed to achieve synchronization. In particular, we have studied how the number of connectors influences the dynamical regime that is set inside the Hele-Shaw cells.
متن کاملذخیره 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: Archive for Rational Mechanics and Analysis
سال: 2022
ISSN: ['0003-9527', '1432-0673']
DOI: https://doi.org/10.1007/s00205-021-01750-4