Browsing Past Topics (PT) by Title
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A variational model for infin ite perimeter segmentations based on lipschitz level set functions: Denoising while keeping finely oscillatory boundaries
(20101231)We propose a new model for segmenting piecewise constant images with irregular object boundaries: a variant of the ChanVese model [T. F. Chan and L. A. Vese, IEEE Trans. Image Process., 10 (2000), pp. 266277], where the ... 
A wellposedness result for hyperbolic operators with Zygmund coefficients
(20131231)In this paper we prove an energy estimate with no loss of derivatives for a strictly hyperbolic operator with Zygmund continuous second order coefficients both in time and in space. In particular, this estimate implies the ... 
About the controlability of some equations in Cardiology, Biology, Fluid Mechanics, and Viscoelasticity
(20140930)In this thesis we analyze the properties of controllability and observability for selected partial differential equations which model various phenomena in cardiology, biology, fluid mechanics and viscoelasticity. We begin, ... 
Aggregation of microglia in 2D with string gradient weighted moving finite elements
(20131231)Alzheimer's disease (AD) is a severe neurodegenerative disorder characterised by cognitive impairment and dementia. In the ADaffected brain, microglia cells are upregulated and accumulate at senile plaques, the most ... 
Air entrainment in transient flows in closed water pipes: A twolayer approach
(20131231)In this paper, we first construct a model for free surface flows that takes into account the air entrainment by a system of four partial differential equations. We derive it by taking averaged values of gas and fluid ... 
Almost periodic parameters for the second moment stability of linear stochastic systems
(20141231)The technical note presents conditions to assure the uniform second moment stability for a class of linear timevarying stochastic systems. The system parameters are assumed to be almost periodic, a concept that is weaker ... 
An ADERtype scheme for a class of equations arising from the waterwave theory
(20160101)In this work we propose a numerical strategy to solve a family of partial differential equations arising from the waterwave theory. These problems may contain four terms; a source which is an algebraic function of the ... 
Analysis and numerical simulations of a chemotaxis model of aggregation of microglia in Alzheimer's disease
(20131231)In this paper, we study the wellposedness in scales of Hilbert spaces Eα, α ∈ ℝ defined by the noncoupled system partial differential operator of a chemotaxis model of aggregation of microglia in Alzheimer's disease for ... 
Approximating travelling waves by equilibria of nonlocal equations
(20121231)We consider an evolution equation of parabolic type in R having a travelling wave solution. We study the effects on the dynamics of an appropriate change of variables which transforms the equation into a nonlocal evolution ... 
Approximation of Hölder continuous homeomorphisms by piecewise affine homeomorphisms
(20111231)This paper is concerned with the problem of approximating a homeomorphism by piecewise affine homeomorphisms. The main result is as follows: every homeomorphism from a planar domain with a polygonal boundary to ℝ2 that is ... 
Approximation of periodic solutions for a dissipative hyperbolic equation
(20131231)This paper studies the numerical approximation of periodic solutions for an exponentially stable linear hyperbolic equation in the presence of a periodic external force f. These approximations are obtained by combining a ... 
Asymptotic expansions for anisotropic heat kernels
(20131231)We obtain the asymptotic expansion of the solutions of some anisotropic heat equations when the initial data belong to polynomially weighted Lpspaces. We mainly address two model examples. In the first one, the diffusivity ... 
Asymptotic limits and stabilization for the 1D nonlinear MindlinTimoshenko system
(20101231)This paper shows how the so called von Kármán model can be obtained as a singular limit of a modified MindlinTimoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... 
Asymptotic stability of rarefaction wave for the navierstokes equations for a compressible fluid in the half space
(20091231)This paper is concerned with the asymptotic stability towards a rarefaction wave of the solution to an outflow problem for the NavierStokes equations in a compressible fluid in the Eulerian coordinate in the half space. ... 
Asymptotic stability of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order
(20091231)In the present article we first study the existence of the stationary solution to an initial boundary value problem for the Mullins equation of fourth order, which was proposed by Mullins ["Twodimensional motion of idealized ... 
Asymptotics and stabilization for dynamic models of nonlinear beams
(20101231)We prove that the von Kármán model for vibrating beams can be obtained as a singular limit of a modified MindlinTimoshenko system when the modulus of elasticity in shear k tends to infinity, provided a regularizing term ... 
Attractors for a class of semilinear degenerate parabolic equations
(20131231)We consider degenerate parabolic equations of the form ∂tu = Δλu + f(u) u{pipe}∂Ω = 0, u{pipe}t=0 = u0 in a bounded domain Ω ⊂N, where Δλ is a subelliptic operator of the type (Formula presented.) We prove global existence ... 
Attractors met Xelliptic operators
(20141231)We consider degenerate parabolic and damped hyperbolic equations involving an operator L, that is Xelliptic with respect to a family of locally Lipschitz continuous vector fields X={X1,... Xm}. The local wellposedness ... 
Averaged control
(20141231)We analyze the problem of controlling parameterdependent systems. We introduce the notion of averaged control according to which the quantity of interest is the average of the states with respect to the parameter. First ... 
Averaged control and observation of parameterdepending wave equations
(20141231)We analyze the problem of averaged observability and control of wave equations.This topic is motivated by the control of parameterdependent systems of wave equations. We look for controls ensuring the controllability of ...