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1.
Improvement of an Estimate of the Global Existence Theorem for Solutions of the Bogoliubov Equations
For a one-dimensional system of particles interacting like elastic balls, we improve an estimate of the existence theorem
for the global solution of the Cauchy problem for the Bogoliubov equations with initial data from the space of sequences of
measurable functions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 145, No. 3, pp. 420–424, December, 2005. 相似文献
2.
N. K. Mamadaliev 《Mathematical Notes》1999,66(3):310-315
A new integral representation of solutions of a Tricomi problem for a strongly degenerate system of equations of parabolic-hyperbolic
type is constructed.
Translated fromMatematicheskie Zametki, Vol. 66, No. 3, pp.385–392, September, 1999. 相似文献
3.
A. P. Chugainova 《Theoretical and Mathematical Physics》2006,147(2):646-659
In the case of nonlinear elastic quasitransverse waves in composite media described by nonlinear hyperbolic equations, we
study the nonuniqueness problem for solutions of a standard self-similar problem such as the problem of the decay of an arbitrary
discontinuity. The system of equations is supplemented with terms describing dissipation and dispersion whose influence is
manifested in small-scale processes. We construct solutions numerically and consider self-similar asymptotic approximations
of the obtained solution of the equations with the initial data in the form of a “spreading” discontinuity for large times.
We find the regularities for realizing various self-similar asymptotic approximations depending on the choice of the initial
conditions including the dependence on the form of the functions determining the small-scale smoothing of the original discontinuity.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 2, pp. 240–256, May, 2006. 相似文献
4.
V. V. Filippov 《Mathematical Notes》1997,61(3):340-345
The verification of an appropriately stated equicontinuity condition for a sequence of solution spaces is one of the two key
points in the theory of the Cauchy problem for equations with singular right-hand sides. We obtain a related sufficient condition.
Translated fromMatematicheskie Zametki, Vol. 61, No. 3, pp. 416–423, March, 1997.
Translated by V. E. Nazaikinskii 相似文献
5.
A. E. Mamontov 《Mathematical Notes》2000,68(3):312-325
The present paper is devoted to the problem of global existence of sufficiently regular solutions to two- and three-dimensional
equations of a compressible non-Newtonian fluid. In the case of the potential stress tensor, we develop a technique for deriving
energy identities that do not contain derivatives of density. On the basis of these identities, in the case of sufficiently
rapidly increasing potentials, we obtain an extended system ofa priori estimates for the equations mentioned above. We also study the related problem of estimating solutions to the nonlinear elliptic
system generated by the stress tensor.
Translated fromMatematicheskie Zametki, Vol. 68, No. 3, pp. 360–376, September, 2000. 相似文献
6.
Yu. S. Kolesov 《Mathematical Notes》1997,62(5):623-628
For a number of meaningful examples, nonresonant wave-type equations are shown to be characterized by periodic dynamics.
Translated fromMatematicheskie Zametki, Vol. 62, No. 5, pp. 744–750, November, 1997.
Translated by O. V. Sipacheva 相似文献
7.
A. V. Gladkov V. V. Dmitrieva R. A. Sharipov 《Theoretical and Mathematical Physics》2000,123(1):436-445
The problem of the reducibility of a system of second-order quasi-linear parabolic differential equations to diffusion-type
equations is considered. An effective solution algorithm is suggested for this problem in the nondegenerate case.
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 123, No. 1, pp. 26–37, April, 2000. 相似文献
8.
Yu. A. Tserkovnikov 《Theoretical and Mathematical Physics》2006,147(3):868-875
We use an example of a chain of equations describing a system of Bose particles with pairwise interaction to develop a method
for decoupling the chain at its second element. We obtain an approximation of the interacting-modes type, which results in
a system of nonlinear equations for one-, two-, and three-particle functions.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 147, No. 3, pp. 503–510, June, 2006. 相似文献
9.
V. I. Ostryk 《Journal of Mathematical Sciences》2009,160(4):453-469
We consider the problem of contact interaction between a semiinfinite stamp with rectilinear base and an elastic strip with
one rigid side. Friction forces in the contact region are taken into account. These forces lead to the division of the contact
region into slipping and adhesion zones. With the use of the Wiener–Hopf method, a system of integral equations is reduced
to an infinite system of algebraic equations. The computational results of stresses and strains at the boundary and at inner
points of the elastic strip are presented.
Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 138–149, January–March, 2008. 相似文献
10.
I. V. Aliev 《Ukrainian Mathematical Journal》2008,60(4):509-520
We investigate the Abel summability of a system of eigenfunctions and associated functions of Bitsadze-Samarskii-type boundary-value
problems for elliptic equations in a rectangle. These problems are reduced to a boundary-value problem for elliptic operator
differential equations with an operator in boundary conditions in the corresponding spaces and are studied by the method of
operator differential equations.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 4, pp. 443–452, April, 2008. 相似文献
11.
M. A. Lyalinov 《Journal of Mathematical Sciences》1998,91(2):2790-2801
A vector electromagnetic problem of diffraction by a wedge-shaped region is reduced to a system of coupled functional equations
by using Sommerfeld integrals. This system of functional equations is solved by the perturbation method, and the convergence
of the related series is analyzed. The system of functional equations is further reduced to linear equations with contracting
operators, and the solution is represented in the form of a Neumann series. Reduction to a system with compact operators is
also considered. Bibliography: 13 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 230, 1995, pp. 138–156.
Translated by M. A. Lyalinov. 相似文献
12.
Yu. R. Romanovskii 《Mathematical Notes》1996,60(1):56-67
The Cartan equivalence method is used to find out if a given equation has a nontrivial Lie group of point symmetries. In particular,
we compute invariants that permit one to recognize equations with a three-dimensional symmetry group. An effective method
to transform the Lie system (the system of partial differential equations to be satisfied by the infinitesimal point symmetries)
into a formally integrable form is given. For equations with a three-dimensional symmetry group, the formally integrable form
of the Lie system is found explicitly.
Translated fromMatematicheskie Zametki, Vol. 60, No. 1, pp. 75–91, July, 1996. 相似文献
13.
Ya. I. Bigun 《Ukrainian Mathematical Journal》1997,49(5):798-804
For a system of quasilinear hyperbolic equations with a system of differential equations with lag, we prove theorems on the
existence and uniqueness of a solution of the Cauchy problem and its continuous dependence on the initial conditions.
Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 49, No. 5, pp. 715–719, May, 1997. 相似文献
14.
V. N. Sushch 《Mathematical Notes》1997,61(5):621-631
Two discrete models of Yang-Mill equations are constructed in the space ℝn for some matrix-valued Lie group. A gauge-invariant discrete model is examined.
Translated fromMatematicheskie Zametki, Vol. 61, No. 5, pp. 742–754, May, 1997.
Translated by O. V. Sipacheva 相似文献
15.
We study the problem of finding conditions for the existence of solutions of weakly nonlinear Noetherian boundary-value problems
for systems of ordinary differential equations and the construction of these solutions. A new iterative procedure with accelerated
convergence is proposed for the construction of solutions of a weakly nonlinear Noetherian boundary-value problem for a system
of ordinary differential equations in the critical case.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1587–1601, December, 2008. 相似文献
16.
A. S. Blagoveshchenskii 《Journal of Mathematical Sciences》1996,79(4):1191-1202
The problem of restoring the velocity of transversal waves in an elastic half-space by a known wave field on the boundary
of a medium is studied. The problem is reduced to a system of “integral” equations similar to the Volterra one. Theorems on
existence in the small and on uniqueness of the solution are proved. Bibliography: 5 titles.
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 203, 1992, pp. 51–67.
Translated by T. N. Surkova. 相似文献
17.
A. I. Shafarevich 《Mathematical Notes》2000,67(6):792-801
Asymptotic solutions whose weak limit has a jump discontinuity on a two-dimensional surface are studied for the Navier-Stokes
equations with small viscosity. The equations describing the leading term of the asymptotics and the correction terms are
obtained and analyzed. A recursive procedure for constructing a formal asymptotic series satisfying the corresponding Cauchy
problem is described.
Translated fromMatermaticheskie Zametki, Vol. 67, No. 6, pp. 938–949, June, 2000. 相似文献
18.
A. O. Danylyuk 《Ukrainian Mathematical Journal》2008,60(12):1889-1900
Using operators of fractional integration and differentiation, we prove a theorem on the wellposedness of a general parabolic
boundary-value problem for a system of integro-differential equations with integral operators in boundary conditions.
Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 60, No. 12, pp. 1610 – 1618, December, 2008. 相似文献
19.
N. G. Marchuk 《Theoretical and Mathematical Physics》2008,157(3):1723-1732
We introduce a new system of equations called a model system of Dirac-Maxwell equations, reproducing the main properties of
the standard system. At the same time, the model system of equations differs from the standard system in several ways; in
particular, it is a tensor system and has a new symmetry with respect to the pseudounitary group. We also propose a version
of the model system of Dirac-Maxwell equations with local (gauge) pseudounitary symmetry. We show that any spinor solution
of the standard system of Dirac-Maxwell equations can be obtained from the corresponding tensor solution of the model system.
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Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 425–435, December, 2008. 相似文献
20.
We consider the direct problem of three-dimensional modeling of marine magnetotelluric sounding of nonhomogeneous media in
the presence of a vertical magnetic field component in the primary field. The problem is reduced to a system of volume integral
equations.
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Translated from Prikladnaya Matematika i Informatika, No. 27, pp. 46–53, 2007. 相似文献