Related papers: On the Kohn-Sham equations with periodic backgroun…
In this paper, we consider the $3$D compressible radiation hydrodynamic (RHD) equations with thermal conductivity in a bounded domain. The existence of unique local strong solutions is firstly established when the initial data are…
In this work we present the convergence of a positivity preserving semi-discrete finite volume scheme for a coupled system of two non-local partial differential equations with cross-diffusion. The key to proving the convergence result is to…
The grand canonical density functional theory for inhomogeneous systems of interacting bosons is developed in the effective action approach. The Legendre transform of the generating functional for Green's functions is used to define the…
We establish the uniqueness of solutions of the Camassa-Holm equation on a finite interval with non-homogeneous boundary conditions in the case of bounded momentum. A similar result for the higher-order Camassa-Holm system is also given.…
This article deals with the convergence of finite volume scheme (FVS) for solving coagulation and multiple fragmentation equations having locally bounded coagulation kernel but singularity near the origin due to fragmentation rates. Thanks…
We study necessary conditions and sufficient conditions for the existence of local-in-time solutions of the Cauchy problem for superlinear fractional parabolic equations. Our conditions are sharp and clarify the relationship between the…
By extrapolating the energies of non-relativistic atoms and their ions with up to 3000 electrons within Kohn-Sham density functional theory, we find that the ionization potential remains finite and increases across a row, even as…
Thermodynamically consistent models for two-phase flow in porous media have attracted significant attention in recent years. In this paper, we prove the existence, uniqueness and regularity of the weak solution to such a recent model…
This paper is concerned with the boundary-value problem on the Boltzmann equation in bounded domains with diffuse-reflection boundary where the boundary temperature is time-periodic. We establish the existence of time-periodic solutions…
Accurate local Kohn-Sham potentials have been constructed for the ground $1s^2 ^1S$ state and, in particular, for the lowest triplet $1s2s ^{3}S$ state of the helium atom, using electron densities from many-body calculations and the…
We consider a class of Cahn-Hilliard equation that models phase separation process of binary mixtures involving nontrivial boundary interactions in a bounded domain with non-permeable wall. The system is characterized by certain dynamic…
We investigate the finite temperature expectation values of the charge and current densities for a complex scalar field with nonzero chemical potential in background of a flat spacetime with spatial topology $R^{p}\times (S^{1})^{q}$. Along…
We study the thermodynamical properties of a one-dimensional gas with one-dimensional gravitational interactions, and placed in a uniform mass background. Periodic boundary conditions are implemented as a modification of the potential…
We consider a discrete time dynamic system described by a difference equation with periodic coefficients and with additive stochastic noise. We investigate the possibility of the periodicity for the solution. In particular, we found…
We prove a uniqueness theorem for compactly supported initial data for the variable speed wave equation arising in models of thermoacoustic tomography, given measurements on a part of the boundary. The proof is based on domain of dependence…
We propose a finite volume scheme for a class of nonlinear parabolic equations endowed with non-homogeneous Dirichlet boundary conditions and which admit relative en-tropy functionals. For this kind of models including porous media…
We evaluate the physical viability and logical strength of an array of putative criteria for big bang singularity resolution in quantum cosmology. Based on this analysis, we propose a mutually consistent set of constitutive conditions,…
Polymer self-consistent field theory techniques are used to derive quantum density functional theory without the use of the theorems of density functional theory. Instead, a free energy is obtained from a partition function that is…
We consider a gas of quasi-free quantum particles confined to a finite box, subjected to singular magnetic and electric fields. We prove in great generality that the finite volume grand-canonical pressure is jointly analytic in the chemical…
This paper concerns the construction and analysis of a numerical scheme for a mixed discrete-continuous fragmentation equation. A finite volume scheme is developed, based on a conservative formulation of a truncated version of the…