相关论文: Donati representation theorem for periodic functio…
This introduction to Green's functions is based on their role as kernels of differential equations. The procedures to construct solutions to a differential equation with an external source or with an inhomogeneity term are put together to…
We study periodic homogenization problems for second-order pde in half-space type domains with Neumann boundary conditions. In particular, we are interested in "singular problems" for which it is necessary to determine both the homogenized…
The electronic properties of disordered systems have been the subject of intense study for several decades. Thermoelectric properties, such as thermopower and thermal conductivity, have been relatively neglected. A long standing problem is…
The quasi-periodic homogenization for some classes of first-order Hamilton-Jaconi-Bellman equation is studied in this paper. The cell problem of the quasi-periodic homogenization satisfies the non-resonance condition, under which the…
We investigate a functional limit theorem (homogenization) for Reflected Stochastic Differential Equations on a half-plane with stationary coefficients when it is necessary to analyze both the effective Brownian motion and the effective…
We develop a theory of the Cauchy problem for linear evolution systems of partial differential equations with the Caputo-Dzrbashyan fractional derivative in the time variable $t$. The class of systems considered in the paper is a fractional…
This paper is devoted to prove the existence of positive solutions of a second order differential equation with a nonhomogeneous Dirichlet conditions given by a parameter dependence integral. The studied problem is a nonlocal perturbation…
This note is a summary of the recent paper [9]. Here, we study the homogenization of elliptic systems with Dirichlet boundary condition, when both the coefficients and the boundary datum are oscillating. In particular, in the paper [9], we…
In this work we revise the most recent developments concerning the study of first order problems regarding differential equations with involutions. We take into account two cases: the case of initial conditions and constant coefficients and…
The dyadic Green's function of the inhomogeneous vector Helmholtz equation describes the field pattern of a single frequency point source. It appears in the mathematical description of many areas of electromagnetism and optics including…
The general idea of this paper is to start from a classical integrable (partial differential) equation which arises as a compatibility condition for a matrix linear differential problem. For definitiveness' sake, a generalised sinh-Gordon…
New necessary and sufficient conditions are given for the quantization of a class of periodic second order non-homogeneous ordinary differential equations in the complex plane in this paper. The problem is studied from the viewpoint of…
We construct an expression for the Green function of a differential operator satisfying nonlocal, homogeneous boundary conditions starting from the fundamental solution of the differential operator. This also provides the solution to the…
If a function $f:\mathbb{R}\to\mathbb{R}$ can be represented as the sum of $n$ periodic functions as $f=f_1+\dots+f_n$ with $f(x+\alpha_j)=f(x)$ ($j=1,\dots,n$), then it also satisfies a corresponding $n$-order difference equation…
Correlation-driven phenomena in molecular periodic systems are challenging to predict computationally not only because such systems are periodically infinite but also because they are typically strongly correlated. Here we generalize the…
The article studies the reiterated homogenization of linear elliptic variational inequalities arising in problems with unilateral constrains. We assume that the coefficients of the equations satisfy and abstract hypothesis covering on each…
This work is devoted to the study of first order linear problems with involution and periodic boundary value conditions. We first prove a correspondence between a large set of such problems with different involutions to later focus our…
The paper deals with homogenization problem for nonlinear elliptic and parabolic equations in a periodically perforated domain, a nonlinear Fourier boundary conditions being imposed on the perforation border. Under the assumptions that the…
We investigate the low energy properties of a correlated metal in the proximity of a Mott insulator within the Hubbard model in two dimensions. We introduce a new version of the Cellular Dynamical Mean Field Theory using cumulants as the…
A linear system of differential equations describing a joint motion of thermoelastic porous body and thermofluid occupying porous space is considered. Although the problem is linear, it is very hard to tackle due to the fact that its main…