From Nash to Cournot-Nash equilibria via the Monge-Kantorovich problem [PDF]
, 2014 The notion of Nash equilibria plays a key role in the analysis of strategic interactions in the framework of $N$ player games. Analysis of Nash equilibria is however a complex issue when the number of players is large.
Blanchet, Adrien, Carlier, Guillaume
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Global stability for the prion equation with general incidence [PDF]
, 2015 We consider the so-called prion equation with the general incidence term introduced in [Greer et al., 2007], and we investigate the stability of the steady states. The method is based on the reduction technique introduced in [Gabriel, 2012]. The argument
Gabriel, Pierre
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Well-posedness and asymptotic behavior of a multidimensional model of morphogen transport [PDF]
, 2011 Morphogen transport is a biological process, occurring in the tissue of living organisms, which is a determining step in cell differentiation. We present rigorous analysis of a simple model of this process, which is a system coupling parabolic PDE with ...
A. Kicheva +9 more
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Nonlinear optimization for a tumor invasion PDE model [PDF]
, 2016 In this work, we introduce a methodology to approximate unknown parameters that appear on a non-linear reaction–diffusion model of tumor invasion. These equations consider that tumor-induced alteration of micro-environmental pH furnishes a mechanism for ...
Fernández Ferreyra, Damián Roberto +3 more
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A mathematical model of systemic inhibition of angiogenesis in metastatic development [PDF]
, 2013 We present a mathematical model describing the time development of a population of tumors subject to mutual angiogenic inhibitory signaling. Based on biophysical derivations, it describes organism-scale population dynamics under the influence of three ...
Benzekry, Sebastien +2 more
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Existence of solutions for the Keller-Segel model of chemotaxis with measures as initial data
, 2015 A simple proof of the existence of solutions for the two-dimensional Keller-Segel model with measures with all the atoms less than $8\pi$ as the initial data is given.
Biler, Piotr, Zienkiewicz, Jacek
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On Kinetic Equations Modeling Evolution of Systems in Mathematical Biology
, 2013 We develop a rigorous formalism for the description of the kinetic evolution of interacting entities modeling systems in mathematical biology within the framework of the evolution of marginal observables.
Fedchun, Yu. Yu., Gerasimenko, V. I.
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Global Existence and Asymptotic Behavior of Solutions to a Chemotaxis-Fluid System on General Bounded Domain [PDF]
, 2014 In this paper, we investigate an initial-boundary value problem for a chemotaxis-fluid system in a general bounded regular domain $\Omega \subset \mathbb{R}^N$ ($N\in\{2,3\}$), not necessarily being convex.
Jiang, Jie, Wu, Hao, Zheng, Songmu
core
Analysis of a mathematical model for the growth of cancer cells
, 2012 In this paper, a two-dimensional model for the growth of multi-layer tumors is presented. The model consists of a free boundary problem for the tumor cell membrane and the tumor is supposed to grow or shrink due to cell proliferation or cell dead.
Kohlmann, Martin
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A simple derivation of BV bounds for inhomogeneous relaxation systems [PDF]
, 2014 We consider relaxation systems of transport equations with heterogeneous source terms and with boundary conditions, which limits are scalar conservation laws. Classical bounds fail in this context and in particular BV estimates.
Perthame, Benoit +2 more
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