相关论文: Two Series Formulae from the Solution of a System …
We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of…
We introduce a simple model of the time evolution of a binary mixture of compressible fluids including the thermal effects. Despite its apparent simplicity, the model is thermodynamically consistent admitting an entropy balance equation. We…
In continuum mechanics, the equations of motion for mixtures are derived through the use of Hamilton's extended principle which regards the mixture as a collection of distinct continua. The internal energy is assumed to be a function of…
The viscous and inviscid aggregation equation with Newtonian potential models a number of different physical systems, and has close analogs in 2D incompressible fluid mechanics. We consider a slight generalization of these equations in the…
We study a second-order parabolic equation with divergence form elliptic operator, having piecewise constant diffusion coefficients with two points of discontinuity. Such partial differential equations appear in the modelization of…
In this paper, we prove two results related to the solutions of norm form equations. Firstly, we give a finiteness result for sums of terms of linear recurrence sequences appearing in the coordinates of solutions of norm form equations.…
Nonlinear dispersionless equations arise as the dispersionless limit of well know integrable hierarchies of equations or by construction, such as the system of hydrodynamic type. Some of these equations are integrable in the Hamiltonian…
This paper presents a family of rapidly convergent summation formulas for various finite sums of analytic functions. These summation formulas are obtained by applying a series acceleration transformation involving Stirling numbers of the…
By means of the telescoping method, we establish two sum- mation formulas on sine function. As the special cases of them, several interesting series expansions for $1/\pi^m$ and $\pi^m$.
The work deals with establishing the solvability of a system of integro-differential equations in the situation of the double scale anomalous diffusion. Each equation of such system involves the sum of the two negative Laplace operators…
In order to provide a formally correct thermodynamical description of inhomogeneous fluids valid on all length scales down to the classical limit we postulate that all extensive quantities have locally extensive analogues. We derive local…
We propose a generalization of equations of quantum mechanics in the hydrodynamic form by introducing the terms taking into account the diffusion velocity at zero and finite temperatures and the density energy of diffusion pressure of the…
This is the second part of the series of papers on symmetry properties of a class of variable coefficient (1+1)-dimensional nonlinear diffusion-convection equations of general form $f(x)u_t=(g(x)A(u)u_x)_x+h(x)B(u)u_x$. At first, we review…
We derive the heat equation for the thermal energy under diffusive space-time scaling for a purely deterministic microscopic dynamics satisfying Newton equations perturbed by an external chaotic force acting like a magnetic field.
In this paper certain classes of infinite sums involving special functions are evaluated analytically by application of basic quantum mechanical principles to simple models of half harmonic oscillator and a particle trapped inside an…
We investigate the two-dimensional ($2$D) inviscid compressible flow equations in axisymmetric coordinates, constrained by an ideal gas equation of state (EOS). Beginning with the assumption that the $2$D velocity field is space-time…
Transport phenomena plays an important role in science and technology. In the wide variety of applications both advection and diffusion may appear. Regarding diffusion, for long times, different type of decay rates are possible for…
With regard to the three basic states of matter (solid, liquid, gas), the calculation of the heat capacity of liquids in a general form has been considered one of the deepest and most interesting challenges in condensed matter physics, due…
We consider combustion problems in the presence of complex chemistry and nonlinear diffusion laws leading to fully nonlinear multispecies reaction-diffusion equations. We establish results of existence of solution and maximum principle,…
A sum rule has been derived for the static pair correlation function. This rule is the extension of the well-known equation that relates density fluctuation to compressibility. The obtained sum rule is applied to the Bose and Fermi ideal…