Regularity of solutions to a lubrication problem with discontinuous separation data

We study the regularity ofthe solution to the Reynolds equation for incompressible and compressible fluids when the gap between the lubricated surfaces, “h(x; y)”, presents a discontinuity in a two-dimensional bounded domain. As in the one-dimensional problem studied by Rayleigh, the solution P does not belong to C1.

Stability of steady states of the Cauchy problem for the exponential reaction-diffusion equation

Abstract We consider the Cauchy problem ut = u + eu, x ∈ RN , t ∈ (0, T ), u(x, 0) = u0, x ∈ RN , where u0 ∈ C(RN ) and T > 0. We first study the radial steady states of the equation and the number of intersections distinguishing four different cases: N = 1, N = 2, 3 N 9 and N 10, writing explicitly every steady state for N = 1 and N = 2. Then we study the large time behavior of solutions of the parabolic problem

On a nonlocal nonlinear ODE arising in magnetic recording.

Abstract In this paper we study the uniqueness of the solution for a nonlinear ODE with nonlocal terms. We consider a limit case of a one-dimensional equation arising in magnetic recording. The equation models the tape deflection where the magnetic head profile, with trenches to control the tape position, is a known function

Mathematical analysis and stability of a chemotaxis model with logistic term.

In this paper we study a non-linear system of dierential equations arising in chemotaxis. The system consists of a PDE that describes the evolution of a population and an ODE which models the concentration of a chemical substance. We study the number of steady states under suitable assumptions, the existence of one global solution to the evolution problem in terms of weak solutions and the stability of the steady states

On a mathematical model of morphogenesis

We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns) similar to the model proposed by Lander, Nie and Wan in 2002.The model consists of a system of two equations: a PDE of parabolic type modeling the distribution of free morphogens with a dynamic boundary condition and an ODE describing the evolution of bound receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We prove existence and uniqueness of solutions and its asymptotic behavior

Mathematical analysis of a model of Morphogenesis: steady states

We consider a simple mathematical model of distribution of morphogens (signaling molecules responsible for the differentiation of cells and the creation of tissue patterns) proposed by Lander, Nie and Wang in 2002. The model consists of a system of two equations: a PDE of parabolic type modeling the distribution of free morphogens and an ODE describing the evolution of bound receptors. Three biological processes are taken into account: diffusion, degradation and reversible binding. We present results concerning the steady states

Stabilization in a two-species chemotaxis system with logistic source

We study a system of three partial differential equations modelling the spatiotemporal behaviour of two competitive populations of biological species both of which are attracted chemotactically by the same signal substance. For a range of the parameters the system possesses a uniquely determined spatially homogeneous positive equilibrium (u?, v?) globally asymptotically stable within a certain nonempty range of the logistic growth coefficients

On the Keller-Segel System with External Application of Chemoattractant

Chemotaxis is the ability of microorganisms to respond to chemical signals by moving along the gradient of the chemical substance, either toward the higher concentration (positive taxis) or away from it (negative taxis)

Asymptotic stability of a two species chemotaxis system with non-diffusive chemoattractant

We study the behavior of two biological populations “u” and “v” attracted by the same chemical substance whose behavior is described in terms of second order parabolic equations. The model considers a logistic growth of the species and the interactions between them are relegated to the chemoattractant production. The system is completed with a third equation modeling the evolution of chemical. We assume that the chemical “w” is a non-diffusive substance and satisfies an ODE, more precisely, {ut=Δu−∇⋅(uχ1(w)∇w)+μ1u(1−u),x∈Ω,t>0,vt=Δv−∇⋅(vχ2(w)∇w)+μ2v(1−v),x∈Ω,t>0,wt=h(u,v,w),x∈Ω,t>0, under appropriate boundary and initial conditions in an n-dimensional open and bounded domain Ω. We consider the cases of positive chemo-sensitivities, not necessarily constant elements. The chemical production function h increases as the concentration of the species “u” and “v” increases. We first study the global existence and uniform boundedness of the solutions by using an iterative approach. The asymptotic stability of the homogeneous steady state is a consequence of the growth of h, χi and the size of μi. Finally, some examples of the theoretical results are presented for particular functions h and χi

A multistrategy approach for digital text

The goal of the research described here is to develop a multistrategy classifier system that can be used for document categorization. The system automatically discovers classification patterns by applying several empirical learning methods to different representations for preclassified documents. The learners work in a parallel manner, where each learner carries out its own feature selection based on evolutionary techniques and then obtains a classification model. In classifying documents, the system combines the predictions of the learners by applying evolutionary techniques as well. The system relies on a modular, flexible architecture that makes no assumptions about the design of learners or the number of learners available and guarantees the independence of the thematic domain