Coexistences: ethics, society, and forms of life. Guest editor’s preface

The article is a preface to the symposium "Coexistences: Ethics, Society, and Forms of Life". It briefly illustrates the conceptual space where the notions of forms of life and coexistencies shape an approach to ethics and social philosophy

Forms of life, forms of reality

The article explores aspects of the notion of forms of life in the Wittgensteinian tradition especially following Iris Murdoch’s lead. On the one hand, the notion signals the hardness and inexhaustible character of reality, as the background needed in order to make sense of our lives in various ways. On the other, the hardness of reality is the object of a moral work of apprehension and deepening to the point at which its distinctive character dissolves into the family of connections we have gained for ourselves. The two movements of thought are connected and necessary

On a nonlinear model for tumor growth in a cellular medium

We investigate the dynamics of a nonlinear model for tumor growth within a cellular medium. In this setting the "tumor" is viewed as a multiphase flow consisting of cancerous cells in either proliferating phase or quiescent phase and a collection of cells accounting for the "waste" and/or dead cells in the presence of a nutrient. Here, the tumor is thought of as a growing continuum $\Omega$ with boundary $\partial \Omega$ both of which evolve in time. The key characteristic of the present model is that the total density of cancerous cells is allowed to vary, which is often the case within cellular media. We refer the reader to the articles \cite{Enault-2010}, \cite{LiLowengrub-2013} where compressible type tumor growth models are investigated. Global-in-time weak solutions are obtained using an approach based on penalization of the boundary behavior, diffusion, viscosity and pressure in the weak formulation, as well as convergence and compactness arguments in the spirit of Lions \cite{Lions-1998} (see also \cite{Feireisl-book, DT-MixedModel-2013}).Comment: 30 pages, 1 figure. arXiv admin note: text overlap with arXiv:1203.1215 by other author

Low Mach number limit for the Quantum-Hydrodynamics system

In this paper we deal with the low Mach number limit for the system of quantum-hydrodynamics, far from the vortex nucleation regime. More precisely, in the framework of a periodic domain and ill-prepared initial data we prove strong convergence of the solutions towards regular solutions of the incompressible Euler system. In particular we will perform a detailed analysis of the time oscillations and of the relative entropy functional related to the system.Comment: To appear in Research in the Mathematical Science