Related papers: Spatially Inhomogeneous Bernstein's Problem and De…
This paper treats the solvability of a semilinear reaction-diffusion system, which incorporates transport (diffusion) and reaction effects emerging from two separated spatial scales: $x$ - macro and $y$ - micro. The system's origin connects…
In this manuscript, we put forth a general scheme for defining initial value problems from Einstein's equations of General Relativity constrained by homogeneous and isotropic expansion. The cosmological models arising as solutions are…
In a recent paper Goriely considers the one--dimensional scalar reaction--diffusion equation $u_t = u_{xx} + f(u)$ with a polynomial reaction term $f(u)$ and conjectures the existence of a relation between a global resonance of the…
Standard models of galaxy formation predict that matter distribution is statistically homogeneous and isotropic and characterized by (i) spatial homogeneity for r<10 Mpc/h, (ii) small-amplitude structures of relatively limited size (i.e.,…
In this short communication, we draw the readers' attention to the inconsistency in the derivation of the Thomson scattering spectrum in inhomogeneous plasma, which leads to violation of the Fluctuation-Dissipation Theorem and a substantial…
In this report we discuss the organization of different levels of nature and the corresponding space-time structures by the consideration of a particular problem of time irreversibility. The fundamental time irreversibility problem consists…
We revisit the homogeneous and inhomogeneous Dirichlet problem for the Laplacian on Lipschitz domains. This is motivated by the recent postings by Amrouche and Moussaoui which purport to contradict known area integral estimates of Dahlberg…
A formulation of Einstein equations is presented that could yield advantages in the study of collisions of binary compact objects during regimes between linear-nonlinear transitions. The key idea behind this formulation is a separation of…
A challenging issue in General Relativity concerns the determination of the manifestly-covariant continuum Hamiltonian structure underlying the Einstein field equations and the related formulation of the corresponding covariant…
In this paper hyperbolic partial differential equations with random coefficients are discussed. Such random partial differential equations appear for instance in traffic flow problems as well as in many physical processes in random media.…
We formulate and discuss a conjecture which would extend a classical inequality of Bernstein.
We resolve a long standing question regarding the suitable effective diffusion coefficient of the spherically-symmetric transport equation, which is valid at long times. To that end, we generalize a transport solution in three dimensions…
In this paper, we study a numerical approximation for a class of stationary states for reaction-diffusion system with m densities having disjoint support, which are governed by a minimization problem. We use quantitative properties of both…
We prove explicit estimates for the error in random homogenization of degenerate, second-order Hamilton-Jacobi equations, assuming the coefficients satisfy a finite range of dependence. In particular, we obtain an algebraic rate of…
We consider Gagliardo-Nirenberg inequalities on the sphere which interpolate between the Poincar\'e inequality and the Sobolev inequality, and include the logarithmic Sobolev inequality as a special case. We establish explicit stability…
Solutions to Einstein's vacuum equations in three dimensions are locally maximally symmetric. They are distinguished by their global properties and their investigation often requires a choice of gauge. Although analyses of this sort have…
What is the probability that all the gas in a box accumulates in the same half of this box? Though amusing, this question underlies the fundamental problem of density fluctuations at equilibrium, which has profound implementations in many…
The isoperimetric problem with a density or weighting seeks to enclose prescribed weighted area with minimum weighted perimeter. According to Chambers' recent proof of the Log Convex Density Conjecture, for many densities on $\mathbb{R}^n$…
A nonlinear diffusion equation is proposed to account for thermalization in fermionic and bosonic systems through analytical solutions. For constant transport coefficients, exact time-dependent solutions are derived through nonlinear…
A semilinear ordinary differential equation is derived from a semilinear Schr\"odinger equation in the homogeneous and isotropic spacetime by the Ehrenfest theorem. The Cauchy problem for the equation is considered. Exact solutions and…