$\delta-$Wave for 1-D and 2-D Hyperbolic Systems

Here a new kind of nonlinear wave, which is called $\delta-$wave, is described by some high resolution difference solutions for Riemann problems of one-dimensional (1-D) and two-dimensional (2-D) nonlinear hyperbolic systems in conservation laws. Some phenomena are numerically shown for the solutions of Riemann problems for 2-D gas dynamics systems.     

一类双曲型一维波动方程反问题解的整体唯一性

本文给出了一类双曲型一维波动方程反问题的解的整体唯一性定理。     

Some Perturbation Problems on 2x2 Nonlinear Hyperbolic Conservation Laws

We study in this paper the perturbation of elementary waves with interactions: overtaking of shock waves belonging to the same characteristic family and penetrating of a shock wave and a rarefaction wave belonging to the different characteristic family for 2 × 2 genuinely nonlinear strictly hyperbolic conservation laws. The entropy solutions for the perturbed problems are obtained by the Glimm's scheme.     

双曲方程的一个反问题

用(E_phHa)代表如下的双曲方程的初一边值问题:设u(x,t)是其解,求满足u(t,ξ)=v(t,ξ)(0qilb)的解.     

THE 2 x 2 Spectral Nevanlinna-Pick Problem

A method is presented to construct interpolation functions intothe 2 x 2 open spectral unit ball. For the spectral Nevanlinna–Pickproblem, these functions are in some sense extremal, and theset of all these interpolation functions is enough to solveany interpolation problem, with solvable finite interpolationdata. This fact is used to compute the complex geodesics forthe symmetrized bidisc and for the spectral unit ball, and tosolve completely the two-point interpolation problem for thetwo target sets.     

双曲型积分微分方程的一个反问题

该文研究了一类双曲型积分微分方程确定未知系数的反问题,利用Ｂａｎａｃｈ压缩映像原理证明了该问题的局部存在唯一性和稳定性。     

一类拟线性双曲组Riemann问题解的不唯一性

本文考虑一类特殊的２×２拟线性守恒律双曲组的二维Ｒｉｅｍａｎｎ问题解的不唯一性，给出解具不唯一性的例子．     

The Riemann Problem for Weakly Perturbed 2 × 2 Hyperbolic Systems

The Cauchy problem for a strictly hyperbolic system of two quasilinear equations with weak perturbation is considered. The asymptotics with respect to a small parameter for a discontinuous solution of the nonperturbed problem is studied. Complete asymptotic expansions are constructed if the solution of the nonperturbed problem involves two shock waves. Bibliography: 4 titles.     

Problem without Boundary Conditions for a Hyperbolic Equation

We consider a mixed problem for a hyperbolic equation with classical initial conditions and two nonlocal integral conditions and prove that it is uniquely solvable. This problem is not self-adjoint; this is an obstruction to applying the usual methods for studying the existence, uniqueness, and stability of its solutions. We reduce this problem to a system whose solvability can be proved by using the contraction mapping principle.__________Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 10, Suzdal Conference-4, 2003.     

About Asymptotic Behavior for a Transmission Problem in Hyperbolic Thermoelasticity

We consider a transmission problem in thermoelasticity with memory. We show the exponential decay of the solution in case of radially symmetric situations, as time goes to infinity.      

Asymptotic Analysis of a Hyperbolic Mixed Problem in One-Dimensional Viscoelasticity

We present an asymptotic analysis of the boundary-generated, small-amplitude, high-frequency waves in a one-dimensional, semi-infinite, viscoelastic solid characterized by a single-integral constitutive functional. The equations governing the wave motion constitute a 2×2 system of hyperbolic Volterra integrodifferential equations. The method of analysis is based on a single-wave expansion of nonlinear geometric optics.     

Calculation of coupling factors for the equation x2ϕ″−(x3+a2x2+a1x+a0)ϕ

A numerical realization of the method of finding coupling factors, described in the author's previous papers, is given in the present paper and its efficiency is studied. It is shown that this method is a generalization of the traditional method of finding coupling factors for Bessel functions. Several relations containing coupling factors are also derived. In a number of cases it is possible to judge the calculation error from the accuracy with which they are satisfied.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 156, pp. 109–124, 1986.     

Hyperbolic Boundary-Value Problem for a Piecewise Homogeneous Hollow Cylinder

Ukrainian Mathematical Journal - By the method of integral and hybrid integral transforms in combination with the method of principal solutions (matrices of influence and Green matrices), we...     

关于一类非线性双曲方程组的二维Cauchy问题

本文通过引进新的广义解定义，对一类非线性双曲方程组的二维Ｃａｕｃｈｙ问题，证明了解的存在唯一性．并且，解可能含δ波．     

A Splitting Iteration Method for a Simple Corank-2 Bifurcation Problem

A splitting iteration method is introduced to approximate a simple corank-2 bifurcation point of a nonlinear equation with small extended systems. This iteration method converges linearly with an adjustable speed and needs little extra computational work.     

On the Existence of a Global Solution of a Hyperbolic Problem

Doklady Mathematics - A quasilinear system of hyperbolic equations describing plane one-dimensional relativistic oscillations of electrons in a cold plasma is considered. For a simplified...     

Two-Dimensional (Two-Speed) Mode for a Nonstrictly Hyperbolic Problem

All types of solutions to the Riemann problem for a system of conservation laws that is nonstrictly hyperbolic in the sense of Petrovskii, but not in the sense of Friedrichs are described.