Results 1 to 10 of about 161 (132)
1-Quasiconformal Mappings and CR Mappings on Goursat Groups [PDF]
The Scientific World Journal, 2014 We show that 1-quasiconformal mappings on Goursat groups are CR or anti-CR mappings. This can reduce the determination of 1-quasiconformal mappings to the determination of CR automorphisms of CR manifolds, which is a fundamental problem in the theory of ...
Qing Yan Wu, Zun Wei Fu
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Solution of a Goursat Problem in Optimal Domains [PDF]
Georgian Mathematical Journal, 2007 Abstract In case a non-linear differential equation is reduced to a fixed-point problem, one has to apply a fixed-point theorem to a suitably chosen subset of the underlying function space. Generally speaking, in view of the non-linearity of the differential equation the restrictions for the data of the problem will be the more extensive
Wolfgang Tutschke
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The Goursat problem for a generalized Helmholtz operator in the plane [PDF]
Journal D'Analyse Mathematique, 2008 We consider the Goursat problem in the plane for partial differential operators whose principal part is the $p$th power of the standard Laplace operator. The data is posed on a union of $2p$ distinct lines through the origin. We show that the solvability of this Goursat problem depends on Diophantine properties of the geometry of lines on which the ...
Hermann Render +2 more
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Mathematics, 2023 In this paper, the method of transmutation operators is used to construct an exact solution of the Goursat problem for a fourth-order hyperbolic equation with a singular Bessel operator.
Sergei M. Sitnik +1 more
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The Goursat problem for hyperbolic linear third order equations
Mathematical Modelling and Analysis, 2001 The third order hyperbolic linear differential equation is considered in the non‐cylindrical domain of multidimensional Euclidean space. The equation operator is a composition of a differentiation operator of the first order and second order operator ...
V. I. Korzyuk
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On the solvability of a semi-periodic boundary value problem for the nonlinear Goursat equation [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2021 In this paper, by means of a change of variables, a nonlinear semi-periodic boundary value problem for the Goursat equation is reduced to a linear gravity problem for hyperbolic equations.
N.T. Orumbayeva +2 more
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Goursat's problem and the holographic principle [PDF]
Nuclear Physics B, 2004 The whole idea of holography as put forward by Gerard 't Hooft assumes that data on a boundary determine physics in the volume. This corresponds to a Dirichlet problem for euclidean signature, or to a Goursat (characteristic) problem in the lorentzian setting. Is this last aspect of the problem that is explored here for Ricci flat spaces with vanishing
Álvarez, Enrique +2 more
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Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2011 The solution of the Goursat problem for the system of the differential equations of the third order is received on the basis of Riemann method. The Riemann matrix expressed in terms of hypergeometric functions with matrix argument is received, using it ...
Aleksander A Andreev, Julia O Yakovleva
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Известия Иркутского государственного университета: Серия "Математика", 2021 The article considers second-order system of linear stochastic partial differential equations of hyperbolic type with Goursat boundary conditions. Earlier, in a number of papers, representations of the solution Goursat problem for linear stochastic ...
K.B. Mansimov, R.O. Mastaliyev
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On Some Non-local Boundary Value and Internal Boundary Value Problems for the String Oscillation Equation [PDF]
Қарағанды университетінің хабаршысы. Математика сериясы, 2023 The work is devoted to the problem of setting new boundary and internal boundary value problems for hyperbolic equations. The consideration of these settings is given on the example of a wave equation.
A.Kh. Attaev
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