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UNIQUENESS CLASSES FOR THE SOLUTION OF GOURSAT'S PROBLEM
Mathematics of the USSR-Izvestiya, 1974Uniqueness classes for the solution of Goursat's problem, which consists in giving Cauchy initial conditions for each of the variables , , are studied for linear partial differential equations with constant coefficients with two groups of variables: time and space .
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ON PROBLEMS REDUCING TO THE GOURSAT PROBLEM FOR A FOURTH ORDER EQUATION
2007In this paper, we investigate some problems which can be reduced to the Goursat problem for a fourth order equation. Some results and theorems are given concerning the existence and uniqence for the solution of the suggested problem. ©Shiraz University.
Maher A., Utkina A.
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ON PROBLEMS REDUCED TO THE GOURSAT PROBLEM FOR A THIRD ORDER EQUATION
2006The aim of the present paper is the investigation of some problems which can be reduced to the Goursat problem for a third order equation. Some results and theorems are given concerning the existence and uniqunce for solving the suggested problem. © Shiraz University.
Maher A., Utkina Y.
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On the numerical solution of the Goursat problem
Applied Mathematics and Computation, 1993The author suggests approximating the Goursat problem, \(u_{xy} = f(x,y,u,u_ x,u_ y)\), by the trapezoidal formula using the harmonic mean for the right hand side. He claims that this gives better results than using the arithmetic or geometric means. His printed results do not appear to support this claim.
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The Goursat and Cauchy Problems for the Sine-Gordon Equation
SIAM Journal on Applied Mathematics, 1978The equivalence of the methods for solving both the Goursat problem and the Cauchy problem for the sine-Gordon equation is discussed. Sufficient conditions on the initial data for which each problem may be solved by the inverse scattering transform are given. It is shown that the inversion procedure for the Goursat problem is slightly more general than
Kaup, David J., Newell, Alan C.
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Generalized goursat problem for a nonlinear differential equation
Ukrainian Mathematical Journal, 1984Translation from Ukr. Mat. Zh. 36, No.1, 110-114 (Russian) (1984; Zbl 0542.35020).
Kovach, Yu. I., Bojtsun, S. A.
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On singular problems of Goursat and Cauchy
Ukrainian Mathematical Journal, 1969Introduction. In this paper the problems of Goursat and Cauchy are investigated for equations of hyperbolic type with singular coefficients. Effective algorithms are presented for constructing Duhamel functions of such singular initial problems, reducing these problems to a recurrent sequence of ordinary linear nonhomogeneous differential equations of ...
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The Goursat problem for Maxwell’s equations
Journal of Mathematical Physics, 1990Using the spinor formalism of electromagnetism, the Goursat problem for Maxell’s equations is defined and some examples of solutions are given.
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The Goursat problem for the homogeneous wave equation
Journal of Mathematical Physics, 1990The Goursat problem for the 3-D homogeneous wave equation is presented and some methods to solve it are discussed.
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