共查询到20条相似文献,搜索用时 15 毫秒
1.
N. A. Watson 《Rendiconti del Circolo Matematico di Palermo》1988,37(1):150-160
We study the behaviour of certain hyperplane mean values of solutions of parabolic equations on an infinite strip, and use
our results to prove a representation theorem for solutions which satisfy a one-sidedL
p constraint. 相似文献
2.
J. Bureš F. Sommen V. Souček P. Van Lancker 《Annals of Global Analysis and Geometry》2002,21(3):215-240
In this paper a generalization of the classicalRarita–Schwinger equations for spin 3/2 fields to the case of spin fieldswith values in irreducible representation spaces with weight k+1/2 isgiven. It corresponds to the study of serie of first orderconformal invariant operators, which are constructed from twisted Diracoperators. The representation character of polynomial solutions of the equations onflat space and their relations are described in details. 相似文献
3.
Peter Berglez 《Annali di Matematica Pura ed Applicata》1986,143(1):155-185
Summary
In the present paper those formally hyperbolic differential equations are characterized for which solutions can be represented by means of differential operators acting on holomorphic functions. This is done by a necessary and sufficient condition on the coefficients of the differential equation. These operators are determined simultaneously. By it a general procedure is presented to construct differential equations and corresponding differential operators which map holomorphic functions onto solutions of the differential equations. We also discuss the question under which circumstances all the solutions of a differential equation can be represented by differential operators. For the equations characterized previously we determine the Riemann function. Some special classes of differential equations are investigated in detail. Furthermore the possibility of a representation of pseudoanalytic functions and the corresponding Vekua resolvents by differential operators is discussed.
Herrn Prof. Dr. K. W. Bauer zum 60. Geburtstag gewidmet 相似文献
Herrn Prof. Dr. K. W. Bauer zum 60. Geburtstag gewidmet 相似文献
4.
A concept of a fundamental solution is introduced for linear operator equations given in some functional spaces. In the case where this fundamental solution does not exist, the representation of the solution is found by the concept of a generalized fundamental solution, which is introduced for operators with nontrivial and generally infinite-dimensional kernels. The fundamental and generalized fundamental solutions are also investigated for a class of Fredholm-type operator equations. Some applications are given for one-dimensional generally nonlocal hyperbolic problems with trivial, finite- and infinite-dimensional kernels. The fundamental and generalized fundamental solutions of such problems are constructed as particular solutions of a system of integral equations or an integral equation. These fundamental solutions become meaningful in a general case when the coefficients are generally nonsmooth functions satisfying only some conditions such as p-integrablity and boundedness. 相似文献
5.
In this paper, the unique solvability of oblique derivative boundary value problems for second order nonlinear equations of mixed (elliptic-hyperbolic) type in multiply connected domains is proved, which mainly is based on the representation of solutions for the above boundary value problem, and the uniqueness and existence of solutions of the above problem for the equation uxx + sgn y uyy = 0. 相似文献
6.
N. I. Ostrosablin 《Journal of Applied and Industrial Mathematics》2013,7(1):89-99
We find a simplest representation for the general solution to the system of the static Lamé equations of isotropic linear elasticity in the form of a linear combination of the first derivatives of three functions that satisfy three independent harmonic equations. The representation depends on 12 free parameters choosing which it is possible to obtain various representations of the general solution and simplify the boundary value conditions for the solution of boundary value problems as well as the representation of the general solution for dynamic Lamé equations. The system of Lamé equations diagonalizes; i.e., it is reduced to the solution of three independent harmonic equations. The representation implies three conservation laws and some formula for producing new solutions which makes it possible, given a solution, to find new solutions to the static Lamé equations by derivations. In the two-dimensional case of a plane deformation, the so-found solution immediately implies the Kolosov-Muskhelishvili representation for shifts by means of two analytic functions of complex variable. Two examples are given of applications of the proposed method of diagonalization of the two-dimensional elliptic systems. 相似文献
7.
V. F. Zhuravlev 《Ukrainian Mathematical Journal》2010,62(2):186-202
On the basis of a generalization of the well-known Schmidt lemma to the case of n-normal and d-normal linear bounded operators in a Banach space, we propose constructions of generalized inverse operators. We obtain criteria
for the solvability of linear equations with these operators and formulas for the representation of solutions of these equations. 相似文献
8.
Bernd Goldschmidt 《Mathematische Nachrichten》1982,107(1):241-251
In a few preceding papers we discussed the existence and representation of solutions of a certain of linear elliptic systems of partial differential equations of first order in the space Rn. Here we construct a complete set of solutions of these systems and prove maximum principles. 相似文献
9.
Denis Constales Rolf Sören Kraußhar 《Mathematical Methods in the Applied Sciences》2009,32(16):2050-2070
In this paper, we study the solutions to the generalized Helmholtz equation with complex parameter on some conformally flat cylinders and on the n‐torus. Using the Clifford algebra calculus, the solutions can be expressed as multi‐periodic eigensolutions to the Dirac operator associated with a complex parameter λ∈?. Physically, these can be interpreted as the solutions to the time‐harmonic Maxwell equations on these manifolds. We study their fundamental properties and give an explicit representation theorem of all these solutions and develop some integral representation formulas. In particular, we set up Green‐type formulas for the cylindrical and toroidal Helmholtz operator. As a concrete application, we explicitly solve the Dirichlet problem for the cylindrical Helmholtz operator on the half cylinder. Finally, we introduce hypercomplex integral operators on these manifolds, which allow us to represent the solutions to the inhomogeneous Helmholtz equation with given boundary data on cylinders and on the n‐torus. Copyright © 2009 John Wiley & Sons, Ltd. 相似文献
10.
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
11.
We deduce a necessary and sufficient condition for the matrix equations AXA*=BB* and CXC*=DD* to have a common Hermitian nonnegative-definite solution and a representation of the general common Hermitian nonnegative-definite solution to these two equations when they have such common solutions. Thereby, we solve a statistical problem which is concerned in testing linear hypotheses about regression coefficients in the multivariate linear model. This paper is a revision of Young et al. (J. Multivariate Anal. 68 (1999) 165) whose mistake was pointed out in (Linear Algebra Appl. 321 (2000) 123). 相似文献
12.
Y. I. Belopolskaya 《Journal of Mathematical Sciences》2000,101(5):3422-3436
It is well known that the relationships between the theory of partial differential equations (PDE) and probability theory
are very deep and allow one to derive new nontrivial results concerning the behavior of random processes and properties of
the solutions of boundary-value problems of PDE. It is natural to make an attempt to construct a probabilistic representation
of the solution of a boundary problem for the Navier-Stokes system and other hydrodynamic equations. We construct such a representation
in terms of a diffusion process. Bibliography: 16 titles.
To O. A. Ladyzhenskaya
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 249, 1997, pp. 77–101.
Translated by Ya. I. Belopolskaya. 相似文献
13.
In this paper, we develop a new representation for outgoing solutions to the time‐harmonic Maxwell equations in unbounded domains in ?3. This representation leads to a Fredholm integral equation of the second kind for solving the problem of scattering from a perfect conductor, which does not suffer from spurious resonances or low‐frequency breakdown, although it requires the inversion of the scalar surface Laplacian on the domain boundary. In the course of our analysis, we give a new proof of the existence of nontrivial families of time‐harmonic solutions with vanishing normal components that arise when the boundary of the domain is not simply connected. We refer to these as k‐Neumann fields, since they generalize, to nonzero wave numbers, the classical harmonic Neumann fields. The existence of k‐Neumann fields was established earlier by Kress. © 2009 Wiley Periodicals, Inc. 相似文献
14.
On the resolution and optimization of a system of fuzzy relational equations with sup-T composition 总被引:3,自引:2,他引:1
This paper provides a thorough investigation on the resolution of a finite system of fuzzy relational equations with sup-T composition, where T is a continuous triangular norm. When such a system is consistent, although we know that the solution set can be characterized
by a maximum solution and finitely many minimal solutions, it is still a challenging task to find all minimal solutions in
an efficient manner. Using the representation theorem of continuous triangular norms, we show that the systems of sup-T equations can be divided into two categories depending on the involved triangular norm. When the triangular norm is Archimedean,
the minimal solutions correspond one-to-one to the irredundant coverings of a set covering problem. When it is non-Archimedean, they only correspond to a subset of constrained irredundant coverings of a set covering problem. We then show that the problem of minimizing a linear objective function subject to a system of sup-T equations can be reduced into a 0–1 integer programming problem in polynomial time. This work generalizes most, if not all,
known results and provides a unified framework to deal with the problem of resolution and optimization of a system of sup-T equations. Further generalizations and related issues are also included for discussion. 相似文献
15.
We prove a Large Deviation Principle for the family of solutions of Volterra equations in the plane obtained by perturbation of the driving white noise. One of the motivations for the study of such class of equations is provided by non-linear hyperbolic stochastic partial differential equations appearing in the construction of some path-valued processes on manifolds. The proof uses the method developped by Azencott for diffusion processes. The main ingredients are exponential inequalities for different classes of two-parameter stochastic integrals; these integrals are related to the representation of the stochastic term in the differential equation as a representable semimatringale. 相似文献
16.
N. E. Barabanov 《Journal of Mathematical Sciences》2007,142(3):2045-2058
The algebraic Lur’e equations are considered in the general case of an arbitrary pair (A, B) and a nonsingular matrix Γ of quadratic form. The necessary and sufficient conditions for the existence of a complete set
of solutions of such equations are obtained. These conditions are other than in the standard case of a definite matrix Γ.
For the standard case, the constraints on the pair (A, B) are maximally relaxed. Then the results are extended to the case of a singular matrix Γ. A special representation of Hamiltonian
matrices, which forms the basis for the proofs, is developed.
__________
Translated from Sovremennaya Matematika i Ee Prilozheniya (Contemporary Mathematics and Its Applications), Vol. 29, Voronezh
Conference-1, 2005. 相似文献
17.
Anthony M. Bloch Peter E. Crouch Jerrold E. Marsden Amit K. Sanyal 《Foundations of Computational Mathematics》2008,8(4):469-500
The purpose of this paper is to extend the symmetric representation of the rigid body equations from the group SO (n) to other groups. These groups are matrix subgroups of the general linear group that are defined by a quadratic matrix identity.
Their corresponding Lie algebras include several classical semisimple matrix Lie algebras. The approach is to start with an
optimal control problem on these groups that generates geodesics for a left-invariant metric. Earlier work by Bloch, Crouch,
Marsden, and Ratiu defines the symmetric representation of the rigid body equations, which is obtained by solving the same
optimal control problem in the particular case of the Lie group SO (n). This paper generalizes this symmetric representation to a wider class of matrix groups satisfying a certain quadratic matrix
identity. We consider the relationship between this symmetric representation of the generalized rigid body equations and the
generalized rigid body equations themselves. A discretization of this symmetric representation is constructed making use of
the symmetry, which in turn give rise to numerical algorithms to integrate the generalized rigid body equations for the given
class of matrix Lie groups.
Dedicated to Professor Arieh Iserles on the Occasion of his Sixtieth Birthday. 相似文献
18.
We give sufficient conditions for the existence of positive solutions to some semilinear elliptic equations in bounded domains
with Dirichlet boundary conditions. We impose mild conditions on the domains and lower order (nonlinear) coefficients of
the equations in that the bounded domains are only required to satisfy an exterior cone condition and we allow the coefficients
to have singularities controlled by Kato class functions. Our approach uses an implicit probabilistic representation, Schauder's
fixed point theorem, and new a priori estimates for solutions of the corresponding linear elliptic equations. In the course
of deriving these a priori estimates we show that the Green functions for operators of the form on D are comparable when one modifies the drift term b on a compact subset of D. This generalizes a previous result of Ancona [2], obtained under an condition on b, to a Kato condition on .
Received: 21 April 1998 / in final form 26 March 1999 相似文献
19.
Monique Laurent 《Mathematical Programming》2007,109(1):1-26
We consider the problem of minimizing a polynomial over a set defined by polynomial equations and inequalities. When the polynomial
equations have a finite set of complex solutions, we can reformulate this problem as a semidefinite programming problem. Our
semidefinite representation involves combinatorial moment matrices, which are matrices indexed by a basis of the quotient
vector space ℝ[x
1, . . . ,x
n
]/I, where I is the ideal generated by the polynomial equations in the problem. Moreover, we prove the finite convergence of a hierarchy
of semidefinite relaxations introduced by Lasserre. Semidefinite approximations can be constructed by considering truncated
combinatorial moment matrices; rank conditions are given (in a grid case) that ensure that the approximation solves the original
problem to optimality.
Supported by the Netherlands Organisation for Scientific Research grant NWO 639.032.203. 相似文献
20.
In this paper after having obtained the Lax pair of a hierarchy of soliton equations,we discuss the parametric representation for finite-band solutions of the stationary solitonequation, and prove it can be represented as a Hamiltonian system which is integrable inLiouville sense. The nonconfocal involutive integral representations {Fm} are obtained also.In the condition of finite-band solutions of the soliton equation, the time and space can bedevided inio two Hamiltonian systems, so the fi… 相似文献