Related papers: Existence and density conservation using a non-con…
In this paper we prove a sharp global existence result for semilinear wave equations with time-dependent scale-invariant damping terms if the initial data is small. More specifically, we consider Cauchy problem of $\partial_t^2u-\Delta…
We obtain new quantitative estimates of the vanishing viscosity approximation for time-dependent, degenerate, Hamilton-Jacobi equations that are neither concave nor convex in the gradient and Hessian entries of the form $\partial_t…
A mathematical model for collision-induced breakage is considered. Existence of weak solutions to the continuous nonlinear collision-induced breakage equation is shown for a large class of unbounded collision kernels and daughter…
Local existence and well posedness for a class of solutions for the Euler Poisson system is shown. These solutions have a density $\rho$ which either falls off at infinity or has compact support. The solutions have finite mass, finite…
Selected theoretical developments in modeling of deposition of submicrometer size (submicron) particles on solid surfaces, with and without surface diffusion, of interest in colloid, polymer, and certain biological systems, are surveyed. We…
In this paper, we study the following nonlinear Schr\"odinger-Poisson type equation \begin{equation*} \begin{cases} -\varepsilon^2\Delta u+V(x)u+K(x)\phi u=f(u)&\text{in}\ \mathbb{R}^3,\\ -\varepsilon^2\Delta \phi=K(x)u^2&\text{in}\…
In this paper, we investigate the constrained minimization problem \begin{equation}\label{eq:0.1} e(a):=\inf_{\{u\in \mathcal{H},\|u\|_2^2=1\}}E_a(u), \end{equation} where the energy functional \begin{equation} \label{eq:0.2}…
This work (Part (I)) together with its companion (Part (II) [45]) develops a new framework for stochastic functional Kolmogorov equations, which are nonlinear stochastic differential equations depending on the current as well as the past…
In this work, we consider the discretization of some nonlinear Fokker-Planck-Kolmogorov equations. The scheme we propose preserves the non-negativity of the solution, conserves the mass and, as the discretization parameters tend to zero,…
A reduced-bias nonparametric estimator of the cumulative distribution function (CDF) and the survival function is proposed using infinite-order kernels. Fourier transform theory on generalized functions is utilized to obtain the improved…
We test the finite density algorithm in the canonical ensemble which combines the HMC update with the accept/reject step according to the ratio of the fermion number projected determinant to the unprojected one as a way of avoiding the…
In this note we continue our study of unidirectional solutions to hydrodynamic Euler alignment systems with strongly singular communication kernels $\phi(x):=|x|^{-(n+\alpha)}$ for $\alpha\in(0,2)$. Here, we consider the critical case…
This paper is concerned with a nonlinear fractional Sch\"ordinger system in $\mathbb{{R}}$ with intraspecies interactions $a_{i}>0 \ (i=1,2)$ and interspecies interactions $\beta \in\mathbb{{R}}$. We study this system by solving an…
The particle mass of dark matter (DM) was previously constrained using kinematics of ultra-faint dwarf galaxies to $m > 3 \times 10^{-19}\,\mathrm{eV}$. This constraint, which excludes the "fuzzy" range of ultra-light dark matter from…
In this paper, we consider the isoperimetric problem in the space $\mathbb{R}^N$ with density. Our result states that, if the density f is l.s.c. and converges to a positive limit at infinity, being smaller than this limit far from the…
Let $\mathcal{A}$ and $\mathcal{B}$ be unital finite-dimensional complex algebras, each equipped with the unique Hausdorff vector topology. Denote by $\mathrm{Max}(\mathcal{A})=\{\mathcal{M}_1, \ldots, \mathcal{M}_p\}$ and…
This paper deals with the derivation of entropy solutions to Cauchy problems for a class of scalar conservation laws with space-density depending fluxes from systems of deterministic particles of follow-the-leader type. We consider fluxes…
We prove an "almost conservation law" to obtain global-in-time well-posedness for the cubic, defocussing nonlinear Schr\"odinger equation in H^s(R^n) when n = 2, 3 and s > 4/7, 5/6, respectively.
We prove existence and multiplicity results for finite energy solutions to the nonlinear elliptic equation \[ -\triangle u+V\left( \left| x\right| \right) u=g\left( \left| x\right| ,u\right) \quad \textrm{in }\Omega \subseteq…
It is shown that the Kadanoff-Baym equations at consistent first-order gradient approximation reveal exact rather than approximate conservation laws related to global symmetries of the system. The conserved currents and energy-momentum…