Browsing Applied Analysis by Title
Now showing items 1-20 of 59
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Asymptotic behavior of the interface for entire vector minimizers in phase transitions
(2022-09-15)We study globally bounded entire minimizers $u:\mathbb{R}^n\rightarrow\mathbb{R}^m$ of Allen-Cahn systems for potentials $W\geq 0$ with $\{W=0\}=\{a_1,...,a_N\}$ and $W(u)\sim |u-a_i|^\alpha$ 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 Many-Body Systems
(2021-10-01)Within this work, we derive and analyse an expression for the free energy of a single-species 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 Shape-Memory Alloys: Some Remarks on Rigidity, Flexibility and Some Numerical Implementations
(2019-03-30)We study convex integration solutions in the context of the modelling of shape-memory 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 Landau-de Gennes study
(2021-01-01)We consider a Landau-de 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 Gamma-convergence discrete-to-continuum approach
(2018-07)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 non-trivial interplay between the topology of the shell and the alignment ... -
Derivation of limit equation for a singular perturbation of a 3D periodic Boussinesq system
(2017-07-15)We consider a system describing the dynamics of an hydrodynamical, density-dependent 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
(2020-02-01)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
(2016-12-14)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
(2017-08)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.
(2021-06-22)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 Beris-Edwards system modeling nematic liquid crystals
(2018-08-10)We consider the Beris-Edwards system modelling incompressible liquid crystal flows of nematic type. This couples a Navier-Stokes system for the fluid velocity with a parabolic reaction-convection-diffusion 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 Sub-Quadratic Potentials
(2021-01-01)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 sub-quadratic behaviour locally near their minima. The corresponding ... -
Entire vortex solutions of negative degree for the anisotropic Ginzburg-Landau system
(2022)The anisotropic Ginzburg-Landau system $\Delta u+\delta \nabla (div u) +\delta curl^*(curl u)=(|u|^2-1) u$, 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 two-dimensional convex bodies: shape reconstruction and non-uniqueness
(2019-02-05)In the Onsager model of one-component hard-particle 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 fluid-structure interaction problem with heat exchange
(2022-01-01)In this paper, we study a nonlinear interaction problem between a thermoelastic shell and a heat-conducting fluid. The shell is governed by linear thermoelasticity equations and encompasses a time-dependent domain which ... -
Fast rotating non-homogeneous fluids in thin domains and the Ekman pumping effect
(2023-10-03)In this paper, we perform the fast rotation limit ε → 0+ of the density-dependent incompressible Navier-Stokes- Coriolis system in a thin strip Ωε := R2×] − lε,lε[, where ε ∈]0,1] is the size of the Rossby number and lε > ... -
Global well-posedness and twist-wave solutions for the inertial Qian-Sheng model of liquid crystals
(2017-10-02)We consider the inertial Qian-Sheng model of liquid crystals which couples a hyperbolic-type equation involving a second-order material derivative with a forced incompressible Navier-Stokes system. We study the energy law ...