Browsing Applied Analysis by Title
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Asymptotic behavior of the interface for entire vector minimizers in phase transitions
(20220915)We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of AllenCahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim ua_i^\alpha$ near $u=a_i$, $0<\alpha<2$. ... 
Asymptotic models for free boundary flow in porous media
(2019)We provide rigorous asymptotic models for the free boundary Darcy and Forchheimer problem under the assumption of weak nonlinear interaction, in a regime in which the steepness parameter of the interface is considered to ... 
Cavity Volume and Free Energy in ManyBody Systems
(20211001)Within this work, we derive and analyse an expression for the free energy of a singlespecies system in the thermodynamic limit in terms of a generalised cavity volume, that is exact in general, and in principle applicable ... 
A comparison principle for vector valued minimizers of semilinear elliptic energy, with application to dead cores
(2021)We establish a comparison principle providing accurate upper bounds for the modulus of vector valued minimizers of an energy functional, associated when the potential is smooth, to elliptic gradient systems. Our assumptions ... 
Convex Integration Arising in the Modelling of ShapeMemory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
(20190330)We study convex integration solutions in the context of the modelling of shapememory alloys. The purpose of the article is twofold, treating both rigidity and flexibility prop erties: Firstly, we relate the maximal ... 
Cubic microlattices embedded in nematic liquid crystals: A Landaude Gennes study
(20210101)We consider a Landaude Gennes model for a connected cubic lattice scaffold in a nematic host, in a dilute regime. We analyse the homogenised limit for both cases in which the lattice of embedded particles presents or not ... 
Defects in Nematic Shells: a Gammaconvergence discretetocontinuum approach
(201807)In this paper we rigorously investigate the emergence of defects on Nematic Shells with a genus different from one. This phenomenon is related to a nontrivial interplay between the topology of the shell and the alignment ... 
Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system
(20170715)We consider a system describing the dynamics of an hydrodynamical, densitydependent flow under the effects of gravitational forces. We prove that if the Froude number is sufficiently small such system is globally well ... 
Design of effective bulk potentials for nematic liquid crystals via colloidal homogenisation
(20200201)We consider a Landau–de Gennes model for a suspension of small colloidal inclusions in a nematic host. We impose suitable anchoring conditions at the boundary of the inclusions, and we work in the dilute regime — i.e. the ... 
Dimension reduction for the micromagnetic energy functional on curved thin films
(20161214)Micromagnetic con gurations of the vortex and onion type have beenwidely studied in the context of planar structures. Recently a signi cant interest to micromagnetic curved thin lms has appeared. In particular, thin ... 
Dispersive effects of weakly compressible and fast rotating inviscid fluids
(201708)We consider a system describing the motion of an isentropic, inviscid, weakly compressible, fast rotating fluid in the whole space $\mathbb{R}^3$, with initial data belonging to $ H^s \left( \mathbb{R}^3 \right), s>5/2 $. ... 
Double layered solutions to the extended Fisher–Kolmogorov P.D.E.
(20210622)We construct double layered solutions to the extended Fisher–Kolmogorov P.D.E., under the assumption that the set of minimal heteroclinics of the corresponding O.D.E. satisfies a separation condition. The aim of our work ... 
Dynamics and flow effects in the BerisEdwards system modeling nematic liquid crystals
(20180810)We consider the BerisEdwards system modelling incompressible liquid crystal flows of nematic type. This couples a NavierStokes system for the fluid velocity with a parabolic reactionconvectiondiffusion equation for the ... 
Effective surface energies in nematic liquid crystals as homogenised rugosity effects
(2021)We study the effect of boundary rugosity in nematic liquid crystalline systems. We consider a highly general formulation of the problem, able to simultaneously deal with several liquid crystal theories. We use techniques ... 
Entire Minimizers of Allen–Cahn Systems with SubQuadratic Potentials
(20210101)We study entire minimizers of the Allen–Cahn systems. The specific feature of our systems are potentials having a finite number of global minima, with subquadratic behaviour locally near their minima. The corresponding ... 
Entire vortex solutions of negative degree for the anisotropic GinzburgLandau system
(2022)The anisotropic GinzburgLandau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(u^21) u$, for $u\colon\mathbb R^2\to\mathbb R^2$ and $\delta\in (1,1)$, models the formation of vortices in liquid crystals. ... 
The excluded volume of twodimensional convex bodies: shape reconstruction and nonuniqueness
(20190205)In the Onsager model of onecomponent hardparticle systems, the entire phase behaviour is dictated by a function of relative orientation, which represents the amount of space excluded to one particle by another at this ... 
Existence of a weak solution to a nonlinear fluidstructure interaction problem with heat exchange
(20220101)In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heatconducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a timedependent domain which ... 
Fast rotating nonhomogeneous fluids in thin domains and the Ekman pumping effect
(20231003)In this paper, we perform the fast rotation limit ε → 0+ of the densitydependent incompressible NavierStokes Coriolis system in a thin strip Ωε := R2×] − lε,lε[, where ε ∈]0,1] is the size of the Rossby number and lε > ... 
Global wellposedness and twistwave solutions for the inertial QianSheng model of liquid crystals
(20171002)We consider the inertial QianSheng model of liquid crystals which couples a hyperbolictype equation involving a secondorder material derivative with a forced incompressible NavierStokes system. We study the energy law ...