Periodic solutions of second-order quasilinear hyperbolic equations

We study a periodic boundary-value problem for a quasilinear equation with the d'Alembert operator on the left-hand side and a nonlinear operator on the right-hand side and establish conditions under which the solution of the indicated problem is unique.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 10, pp. 1370–1375, October, 1995.     

Application of the variation principle for the problem of buckling of a nonlinearly elastic ring nonuniform along its thickness

There has been considerable recent attention given to the stressed and buckled states of items with complicated configuration made of different nonlinearly elastic materials joined by complete adhesion. However, effective analytical solutions for such problems have been hindered by mathematical difficulties. Approximate methods have thus been developed for such problems. A variational combined principle has been formulated in this communication. A nonlinear geometrical approach has been used for formulating a mixed-type functional with physical relationships given by Euler equations, nonlinear equilibrium equations, and nonlinear boundary conditions for a piecewise-nonuniform nonlinearly elastic body composed of finite elements (particles). As an example, buckling along the nonuniform thickness of nonlinearly elastic rings was analyzed hypothetically assuming plane cross-sections. Options for two-, three-, four-, five-, and six-layered rings in a periodical structure have been reviewed. The critical buckling forces for an even number of layers have been found to be equal to each other. The ratios of the critical forces, elasticity moduli, and proportionality levels were determined for all five variants by the Runge-Kutta method.Presented at the Ninth International Conference on the Mechanics of Composite Materials (Riga, October, 1995).Translated from Mekhanika Kompozitnykh Materialov, Vol. 31, No. 2, pp. 262–268, March–April, 1995.     

On the mechanism of phenol ozonolysis

The mechanisms of liquid-phase phenol ozonation are revised. A new mechanism in which a significant role is played by free-radical reactions is suggested for this process.     

Charm production in two-photon collisions: Calculation of the leading nonperturbative contribution in QCD

The leading nonperturbative contribution to the cross section of charm production in two-photon collisions is calculated in QCD. Operator expansion is used and the c-quark interaction with vacuum gluon condensate is taken into account. As a result, the moments of the charm contribution to the photon structure function are obtained. The moments with sufficiently high numbers turn out to be sensitive to the gluon condensate.     

Numerical investigation of the heating of condensed media by volume heat sources

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 22–28, November–December, 1992.     

Heat and mass transport in bundles that move and give off gas

Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, No. 6, pp. 96–103, November–December, 1992.     

Initial-Boundary Value Problem for the Reynolds Lubrication Equation

The nonstationary Reynolds equation of the theory of gas lubrication is considered. The existence and uniqueness of a solution to the initial-boundary value problem for this equation are established in the case of sufficiently smooth data. Estimates for the solution are obtained for large bearing numbers. Bibliography: 8 titles.