Basic boundary-value problems for one equation with fractional derivatives

We prove certain properties of solutions of the equation

Vibrations of Elastic Strings: Mathematical Aspects, Part Two

Dedicated to Professor Jacque-Louis Lions on the occasion of his 70th birthday We consider a mixed problem for the operator

Null-sets ofH-solutions

We considerC ²-solutionsf=u+iv+jw of the system

Existence,uniqueness and convergence as vanishing viscosity for a reaction-diffusion-convection system

A simple qualitative model of dynamic combustion

Linear differential operators related to the Jacobian Conjecture have a closed image

The main result of this work is the following theorem: LetP,QɛC[x, y] satisfy the Jacobian identity

Inequalities for the Volume of the Unit Ball in \mathbb {R}^{n}, II

We present several sharp inequalities for the volume of the unit ball in ,

FINITE TRAVELING WAVES FOR A REACTION-DIFFUSION SYSTEM WITH N（≥3） COMPONENTS

ＦＩＮＩＴＥＴＲＡＶＥＬＩＮＧＷＡＶＥＳＦＯＲＡＲＥＡＣＴＩＯＮ┐ＤＩＦＦＵＳＩＯＮＳＹＳＴＥＭＷＩＴＨＮ（３）ＣＯＭＰＯＮＥＮＴＳＷＡＮＧＳＨＵ,ＷＥＮＳＨＩＨＬＩＡＮＧＡＮＤＹＥＱＩＸＩＡＯＡｂｓｔｒａｃｔ．Ｉｎｔｈｉｓｐａｐｅｒ,ｔｈｅｅｘ...     

Small Ball Asymptotics for the Stochastic Wave Equation

We examine the small ball asymptotics for the weak solution X of the stochastic wave equation

Brownian motion with negative drift and convex level sets in space-time

Suppose a, b, and are reals witha<b and consider the following diffusion equation

Compactification of supports of energy weak solutions to quasilinear parabolic equations of nonstationary filtration type with strong convection

The paper deals with localization properties of solutions to the Cauchy problem with the initial data u₀(x) ∈ L₂(ℝ_n) for a wide class of equations in the divergence form. This class contains, e.g., the following equation:

<Emphasis Type="Italic">L</Emphasis><Superscript><Emphasis Type="Italic">q</Emphasis></Superscript>-Functional Inequalities and Weighted Porous Media Equations

Using measure-capacity inequalities we study new functional inequalities, namely L ^q -Poincaré inequalities

Explicit formulas for spectral characteristics and solutions of the sh-Gordon equation

To the sh-Gordon equation

Equivalent definition of some weighted Hardy spaces

We present an equivalent definition of functions analytic in the half-plane ℂ₊ = {z: Re z > 0} for which

Time-periodic solutions of dissipative ε-approximations for modified Navier-Stokes equations

In this paper, the existence “in the large” of time-periodic classical solutions (with period T) is proved for the following two dissipative ε-approximations for the Navier-Stokes equations modified in the sense of O. A. Ladyzhenskaya:

Diffusion instability of a uniform cycle bifurcating from a separatrix loop

We consider the boundary value problem

Bounds for the Third Peano Constants of Gaussian Quadrature Formulae

Denote by R _n ^G the remainder functional of the Gaussian quadrature formula involving n nodes. Using an elementary method, we derive the asymptotically best possible inequalities

Estimates for eigenvalues of Laplacian operator with any order

Let D be a bounded domain in an n-dimensional Euclidean space Rn. Assume that 0 ＜ λ1 ≤λ2 ≤ … ≤ λκ ≤ … are the eigenvalues of the Dirichlet Laplacian operator with any order l{(-△)lu=λu, in D u=(δ)u/(δ)(→n)=…(δ)l-1u/(δ)(→n)l-1=0,on (δ)D.Then we obtain an upper bound of the (k 1)-th eigenvalue λκ 1 in terms of the first k eigenvalues.k∑i=1(λκ 1-λi) ≤ 1/n[4l(n 2l-2)]1/2{k∑i=1(λκ 1-λi)1/2λil-1/l k∑i=1(λκ 1-λi)1/2λ1/li}1/2.This ineguality is independent of the domain D. Furthermore, for any l ≥ 3 the above inequality is better than all the known results. Our rusults are the natural generalization of inequalities corresponding to the case l = 2 considered by Qing-Ming Cheng and Hong-Cang Yang. When l = 1, our inequalities imply a weaker form of Yang inequalities. We aslo reprove an implication claimed by Cheng and Yang.     

Connection between the kinetic equations and the equations of hydrodynamics

One investigates the Cauchy problem for the nonlinear Boltzmann equation

On the Correctness of the Dirichlet Problem in a Characteristic Rectangle for Fourth Order Linear Hyperbolic Equations

It is proved that the Dirichlet problem is correct in the characteristic rectangle D _ab = [0, a] × [0, b] for the linear hyperbolic equation

On Existence and Multiplicity of Solutions for Elliptic Equations Involving the p-Laplacian

In the present paper, the following Dirichlet problem and Neumann problem involving the p-Laplacian