Browsing Past Topics (PT) by Title
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Counterexample of loss of regularity for fractional order evolution equations with both degenerating and oscillating coefficients
(20141231)For weak evolution models of fractional order with singularity near the origin, the joint influence from the principal œÉLaplacian operator, degenerating part and oscillating part is of prime concern in the discussion of ... 
Critical points and symmetries of a free energy function for biaxial nematic liquid crystals
(20151231)We describe a general mean field model for the free energy function for a homogeneous medium of mutually interacting molecules, based on the formalism for a biaxial nematic liquid crystal set out by Katriel et al (1986) ... 
Derivation of a homogenized nonlinear plate theory from 3d elasticity
(20141231)We derive, via simultaneous homogenization and dimension reduction, the (Formula presented.)limit for thin elastic plates whose energy density oscillates on a scale that is either comparable to, or much smaller than, the ... 
Derivation of a homogenized vonKármán plate theory from 3D nonlinear elasticity
(20131231)We rigorously derive a homogenized vonKármán plate theory as a Γlimit from nonlinear threedimensional elasticity by combining homogenization and dimension reduction. Our starting point is an energy functional that ... 
Derivation of a homogenized vonKármán shell theory from 3D elasticity
(20141231)We derive homogenized von Kármán shell theories starting from three dimensional nonlinear elasticity. The original three dimensional model contains two small parameters: the period of oscillation $\epsilon$ of the material ... 
A direct algorithm in some free boundary problems
(20160628)In this paper we propose a new algorithm for the well known elliptic obstacle problem and for parabolic variational inequalities like one and two phase Stefan problem and of obstacle type. Our approach enters the category ... 
Dispersion for 1d Schrödinger and wave equations with bv coefficients
(20160101)In this paper we analyze the dispersion for one dimensional wave and Schrödinger equations with BV coefficients. In the case of the wave equation we give a complete answer in terms of the variation of the logarithm of the ... 
Dispersion for the Schrödinger equation on networks
(20111231)In this paper, we consider the Schrödinger equation on a network formed by a tree with the last generation of edges formed by infinite strips. We give an explicit description of the solution of the linear Schrödinger ... 
Dispersive Properties for Discrete Schrödinger Equations
(20111231)In this paper we prove dispersive estimates for the system formed by two coupled discrete Schrödinger equations. We obtain estimates for the resolvent of the discrete operator and prove that it satisfies the limiting ... 
Emergence of cooperation in phenotypically heterogeneous populations: A replicator dynamics analysis
(20151231)The emergence of cooperation is analyzed in heterogeneous populations where two kinds of individuals exist according to their phenotypic appearance. Phenotype recognition is assumed for all individuals: individuals are ... 
Emerging properties of financial time series in the "game of Life"
(20111231)We explore the spatial complexity of Conway's "Game of Life," a prototypical cellular automaton by means of a geometrical procedure generating a twodimensional random walk from a bidimensional lattice with periodical ... 
Estimating the division rate of the growthfragmentation equation with a selfsimilar kernel
(20141231)We consider the growthfragmentation equation and we address the problem of estimating the division rate from the stable size distribution of the population, which is easily measured, but nonsmooth. We propose a method ... 
Exact Controllability of the Time Discrete Wave Equation: A Multiplier Approach
(20101231)In this paper we summarize our recent results on the exact boundary controllability of a trapezoidal time discrete wave equation in a bounded domain. It is shown that the projection of the solution in an appropriate space ... 
Existence and regularity of weak solutions to a model for coarsening in molecular beam epitaxy
(20131231)Taking into account the occurrence of a zero of the surface diffusion current and the requirement of the EhrlichSchwoebel effect, Siegert et al. formulated a model of Langevin type that describes the growth of pyramidlike ... 
Existence of a global weak solution to Compressible Primitive Equations
(20121231)In this Note, we show a global weak existence result for a two dimensional Compressible Primitive Equations for atmosphere dynamics modeling. 
Existence of Global Strong Solutions in Critical Spaces for Barotropic Viscous Fluids
(20111231)This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≧ 2. We address the question of the global existence of strong solutions for initial data close to a constant state having ... 
Existence of strong solutions in critical spaces for barotropic viscous fluids in larger spaces
(20121231)This paper is dedicated to the study of viscous compressible barotropic fluids in dimension N ≥ 2. We address the question of wellposedness for large data having critical Besov regularity. Our result improves the analysis ... 
Existence, uniqueness and asymptotic behavior of the solutions to the fully parabolic KellerSegel system in the plane
(20141231)In the present article we consider several issues concerning the doubly parabolic KellerSegel system (1.1)(1.2) in the plane, when the initial data belong to critical scalinginvariant Lebesgue spaces. More specifically, ... 
Explicit 2D ∞harmonic maps whose interfaces have junctions and corners
(20131231)Given a map u:Ω⊆Rn→RN, the ∞Laplacian is the system:(1)δ∞u:=(Du⊗Du+Du2[Du]⊥⊗I):D2u=0 and arises as the "EulerLagrange PDE" of the supremal functional E∞(u,Ω)={norm of matrix}Du{norm of matrix}L∞(Ω). (1) is the model ... 
Explicit energyminimizers of incompressible elastic brittle bars under uniaxial extension [Minimiseurs de l'énergie explicits d'une barre incompressible, élastique, mais fragile, soumise à une extension uniaxiale]
(20101231)A rectangular bar made of a hyperelastic, but brittle, incompressible homogeneous and isotropic material is subject to uniaxial extension. We prove that the energy minimizers are, depending on the toughness coefficient of ...