共查询到20条相似文献,搜索用时 31 毫秒
1.
We pose and investigate the Riemann boundary-value problem for regular and strongly regular functions in Clifford algebras. The posed problem is reduced to the matrix problem for analytical functions in one and two complex variables and we give its solution. We carry out the boundary-value problems in special cases. 相似文献
2.
Anatolii A. Karatsuba Ekatherina A. Karatsuba 《Functional Analysis and Other Mathematics》2011,3(2):113-125
The paper is about the problem of carefully estimating the bounds, which is sometimes missing in the theoretical physics.
Possible consequences of the missing of the bounds is discussed on example of the Riemann zeta function. The text of the paper
is based on the drafts of A.A. Karatsuba’s lecture “Physical mathematics in number theory”, devoted to the 85th birthday of
academician Vasilii Sergeevich Vladimirov. 相似文献
3.
Stevan Pilipovic 《Mathematische Nachrichten》1988,137(1):19-25
The quasiasymptotic of distributions with the supports in (0, ∞) was studied by the Soviet mathematicians Vladimirov, Dro?inov and Zavialov in several papers. Some essential questions on the quasiasymptotic behaviour of Schwartz distributions defined on R are posed and answered in this paper. 相似文献
4.
《Journal of Applied Mathematics and Mechanics》2007,71(1):20-29
For problems of the mechanics of an anisotropic inhomogeneous continuum, theorems are given concerning the uninterrupted symmetrical and antisymmetrical analytical continuation of the solution through the plane part of the boundary surface of the medium. Theorems are given for two types of mechanics problem; in the first of these both symmetrical and antisymmetrical continuations of the solution are allowed, while in the second only symmetrical continuation of the solution is allowed. Problems of the first type include problems which are reduced to linear thermoelastic dynamic differential equations of motion of an inhomogeneous anisotropic medium possessing a plane of elastic symmetry, to linear thermoelastic dynamic differential equations of motion of an inhomogeneous Cosserat medium, to non-linear differential equations describing the static elastoplastic stress state of a plate, etc. The second type includes problems which are reduced to non-linear differential equations describing geometrically non-linear strains of shells, to Navier–Stokes equations, etc. These theorems extend the principle of mirror reflection (the Riemann–Schwartz principle of symmetry) to linear and non-linear equations of continuum mechanics. The uninterrupted continuation of the solutions is used to solve problems of the equilibrium state of bodies of complex shape. 相似文献
5.
In this article,we consider a class of compound vector-valued problem on upper-half plane C+,which consists of vector Riemann problem along a closed contour in C+ with matrix coefficient in Hlder class and vector Hilbert problem on the real axis with essential bounded measurable matrix coefficient.Under appropriate assumption we obtain its solution by use of Corona theorem and factorization of matrix functions in decomposed Banach algebras. 相似文献
6.
S. I. Bezrodnykh 《Mathematical Notes》2017,101(5-6):759-777
The solution of the Riemann–Hilbert problem for an analytic function in a canonical domain for the case in which the data of the problem is piecewise constant can be expressed as a Christoffel–Schwartz integral. In this paper, we present an explicit expression for the parameters of this integral obtained by using a Jacobi-type formula for the Lauricella generalized hypergeometric function F D (N). The results can be applied to a number of problems, including those in plasma physics and the mechanics of deformed solids. 相似文献
7.
In this paper,firstly,by solving the Riemann problem of the zero-pressure flow in gas dynamics with a flux approximation,we construct parameterized delta-shock and constant density solutions,then we show that,as the flux perturbation vanishes,they converge to the delta-shock and vacuum state solutions of the zero-pressure flow,respectively.Secondly,we solve the Riemann problem of the Euler equations of isentropic gas dynamics with a double parameter flux approximation including pressure.Furthermore,we rigorously prove that,as the two-parameter flux perturbation vanishes,any Riemann solution containing two shock waves tends to a delta-shock solution to the zero-pressure flow;any Riemann solution containing two rarefaction waves tends to a two-contact-discontinuity solution to the zero-pressure flow and the nonvacuum intermediate state in between tends to a vacuum state.Finally,numerical results are given to present the formation processes of delta shock waves and vacuum states. 相似文献
8.
Max Glick 《Advances in Mathematics》2011,227(2):1
The pentagram map, introduced by R. Schwartz, is defined by the following construction: given a polygon as input, draw all of its “shortest” diagonals, and output the smaller polygon which they cut out. We employ the machinery of cluster algebras to obtain explicit formulas for the iterates of the pentagram map. 相似文献
9.
Cauchy problem on non-globally hyperbolic space-times 总被引:1,自引:0,他引:1
I. Ya. Aref’eva T. Ishiwatari I. V. Volovich 《Theoretical and Mathematical Physics》2008,157(3):1646-1654
We consider solutions of the Cauchy problem for hyperbolic equations on non-globally hyperbolic space-times containing closed
timelike curves (time machines). We prove that for the wave equation on such space-times, there exists a solution of the Cauchy
problem that is discontinuous and in some sense unique for arbitrary initial conditions given on a hypersurface at a time
preceding the formation of closed timelike curves. If the hypersurface of initial conditions intersects the region containing
closed timelike curves, then the solution of the Cauchy problem exists only for initial conditions satisfying a certain self-consistency
requirement.
To Vasilii Sergeevich Vladimirov with best wishes on his 85th birthday
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 157, No. 3, pp. 334–344, December, 2008. 相似文献
10.
We study boundary value problems posed in a semistrip for the elliptic sine-Gordon equation, which is the paradigm of an elliptic integrable PDE in two variables. We use the method introduced by one of the authors, which provides a substantial generalization of the inverse scattering transform and can be used for the analysis of boundary as opposed to initial-value problems. We first express the solution in terms of a 2×2 matrix Riemann–Hilbert problem whose “jump matrix” depends on both the Dirichlet and the Neumann boundary values. For a well posed problem one of these boundary values is an unknown function. This unknown function is characterised in terms of the so-called global relation, but in general this characterisation is nonlinear. We then concentrate on the case that the prescribed boundary conditions are zero along the unbounded sides of a semistrip and constant along the bounded side. This corresponds to a case of the so-called linearisable boundary conditions, however, a major difficulty for this problem is the existence of non-integrable singularities of the function q y at the two corners of the semistrip; these singularities are generated by the discontinuities of the boundary condition at these corners. Motivated by the recent solution of the analogous problem for the modified Helmholtz equation, we introduce an appropriate regularisation which overcomes this difficulty. Furthermore, by mapping the basic Riemann–Hilbert problem to an equivalent modified Riemann–Hilbert problem, we show that the solution can be expressed in terms of a 2×2 matrix Riemann–Hilbert problem whose “jump matrix” depends explicitly on the width of the semistrip L, on the constant value d of the solution along the bounded side, and on the residues at the given poles of a certain spectral function denoted by h(λ). The determination of the function h remains open. 相似文献
11.
In this paper the Wiener–Hopf (or Riemann–Hilbert) factorization of a class of symbols important in applications is studied. The symbols in this class involve outer functions that appear in applications such as diffraction by strip gratings and infinite-dimensional integrable systems. The method proposed is based on the reduction of a vector Riemann–Hilbert to a scalar problem on an appropriate Riemann surface. Two examples are given leading to the Riemann sphere and to an elliptic curve. 相似文献
12.
Robert F Millar 《Journal of Mathematical Analysis and Applications》1980,76(2):498-515
An explicit representation is derived for the continuation across an analytic boundary of the solution to a boundary value problem for an analytic elliptic equation of second order in two independent variables. The representation is in terms of Cauchy data on the boundary and the complex Riemann function. This is equivalent to a representation for the solution to Cauchy's problem given by Henrici in 1957. It is confirmed that the method of complex characteristics is satisfactory for locating real singularities in the solution provided that the Riemann function is entire in its four arguments. Applications to Laplace's and Helmholtz's equations are discussed. By inserting known, simple solutions to the latter equation into the representation formula, several nontrivial integral relations involving the Bessel function J0, and a possibly new series expansion for Jμ(x), are found. 相似文献
13.
John M. Hong 《Journal of Differential Equations》2006,222(2):515-549
We construct a generalized solution of the Riemann problem for strictly hyperbolic systems of conservation laws with source terms, and we use this to show that Glimm's method can be used directly to establish the existence of solutions of the Cauchy problem. The source terms are taken to be of the form a′G, and this enables us to extend the method introduced by Lax to construct general solutions of the Riemann problem. Our generalized solution of the Riemann problem is “weaker than weak” in the sense that it is weaker than a distributional solution. Thus, we prove that a weak solution of the Cauchy problem is the limit of a sequence of Glimm scheme approximate solutions that are based on “weaker than weak” solutions of the Riemann problem. By establishing the convergence of Glimm's method, it follows that all of the results on time asymptotics and uniqueness for Glimm's method (in the presence of a linearly degenerate field) now apply, unchanged, to inhomogeneous systems. 相似文献
14.
In this paper, we are concerned with the existence and uniqueness of the local solution to the generalized Riemann problem
for first order quasi-linear hyperbolic systems of conservation laws in the presence of the shock wave with large amplitude
and the centered wave. Apart from some exceptions, we prove the problem admits a unique piecewise smooth solution u=u(t,x), and this solution has a structure similar to the similarity solution u=u(x/t) of the corresponding Riemann problem in the neighborhood of the origin, provided that the coefficients of the system and
the initial conditions are sufficiently smooth. The application of our results in rich system is also given. 相似文献
15.
Wenhua SUN~* Wancheng SHENG~ 《数学年刊B辑(英文版)》2007,28(6):701-708
The non-selfsimilar Riemann problem for two-dimensional zero-pressure flow in gas dynamics with two constant states separated by a convex curve is considered.By means of the generalized Rankine-Hugoniot relation and the generalized characteristic analysis method,the global solution involving delta shock wave and vacuum is constructed.The explicit solution for a special case is also given. 相似文献
16.
17.
A generalization of the Riemann problem for gas dynamical flows influenced by curved geometry, such as flows in a variable-area duct, is solved. For this generalized Riemann problem the initial data consist of a pair of steady-state solutions separated by a jump discontinuity. The solution of the generalized Riemann problem is used as a basis for a random choice method in which steady-state solutions are used as an Ansatz to approximate the spatial variation of the solution between grid points. For nearly steady flow in a Laval nozzle, where this Ansatz is appropriate, this generalized random choice method gives greatly improved results. 相似文献
18.
An algebraically expandable class is a class of similar algebras axiomatizable by sentences of the form ${(\forall\exists ! \bigwedge eq)}$ . The problem investigated in this work is that of finding all algebraically expandable classes within a given variety. A complete solution is presented for a number of varieties, including the classes of Boolean algebras, Stone algebras, semilattices, distributive lattices and generalized Kleene algebras. We also study the problem for the case of discriminator varieties, where we prove that there is a lattice isomorphism between the lattice of all algebraically expandable classes of the variety and a certain lattice of subclasses of the simple members of the variety. Finally this connection is applied to calculating the algebraically expandable subclasses of the varieties of monadic algebras and P-algebras. 相似文献
19.
A. M. Meirmanov 《Proceedings of the Steklov Institute of Mathematics》2008,261(1):204-213
We study applications of a new class of infinite-dimensional Lie algebras, called Lax operator algebras, which goes back to the works by I. Krichever and S. Novikov on finite-zone integration related to holomorphic vector bundles
and on Lie algebras on Riemann surfaces. Lax operator algebras are almost graded Lie algebras of current type. They were introduced
by I. Krichever and the author as a development of the theory of Lax operators on Riemann surfaces due to I. Krichever, and
further investigated in a joint paper by M. Schlichenmaier and the author. In this article we construct integrable hierarchies
of Lax equations of that type.
Published in Russian in Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2008, Vol. 263, pp. 216–226.
Dedicated to S.P. Novikov on the occasion of his 70th birthday 相似文献
20.
The initial-boundary value problem for the KdV equation on a finite interval is analyzed in terms of a singular Riemann–Hilbert problem for a matrix-valued function in the complex k-plane which depends explicitly on the space–time variables. For an appropriate set of initial and boundary data, we derive the k-dependent “spectral functions” which guarantee the uniqueness of Riemann–Hilbert problem's solution. The latter determines a solution of the initial-boundary value problem for KdV equation, for which an integral representation is given. To cite this article: I. Hitzazis, D. Tsoubelis, C. R. Acad. Sci. Paris, Ser. I 347 (2009). 相似文献