Results 31 to 40 of about 6,408,424 (182)

Solution of a Goursat Problem in Optimal Domains [PDF]

gmj, 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
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Goursat problem in Hyperbolic partial differential equations with variable coefficients solved by Taylor collocation method [PDF]

Iranian Journal of Numerical Analysis and Optimization
The hyperbolic partial differential equation (PDE) has important practical uses in science and engineering. This article provides an estimate for solving the Goursat problem in hyperbolic linear PDEs with variable coefficients.
F. Birem, A. Boulmerka, H. Laib, C. Hennous   +3 more
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Goursat’s problem on the plane for a quasilinear hyperbolic equation

Doklady of the National Academy of Sciences of Belarus, 2022
A classical solution of the problem for a quasilinear hyperbolic equation in the case of two independent variables with given conditions for the desired function on the characteristic lines is obtained. The problem is reduced to a system of equations with a completely continuous operator.
Korzyuk, Viktor Ivanovich, Kovnatskaya, Ol'ga Anatol'evna, Sevastyuk, Vladimir Aleksandrovich   +2 more
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Uniqueness Theorems for Goursat-Type Problems

Journal of Differential Equations, 1994
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mishnaevskii, P.A., Ramm, A.G.
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Existence and uniqueness of nonlinear Goursat problem in the class of Denjoy–Carleman

Partial Differential Equations in Applied Mathematics
The problem of existence and uniqueness of nonlinear Goursat is studied by Claude Wagschal in different spaces: holomorphic spaces, partially holomorphic, continuous-Gevrey and Gevrey-holomorphic.
Smail Latreche, Kaddour Guerbati, Rafik Guefaifia, Ibrahim Mekawy, Asma Alharbi, Rashid Jan   +5 more
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ON MATHEMATICAL MODELS OF THE ALLER EQUATION

Vestnik KRAUNC: Fiziko-Matematičeskie Nauki, 2016
The solution to the Goursat problem is written out explicitly for a hyperbolic secondorder loaded equation, proposed as a mathematical model of Aller equation under certain conditions.
Khubiev K. U.
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The characteristic problem for the system of the general hyperbolic differential equations of the third order with nonmultiple characteristics

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2013
We consider the well-posed characteristic problem for the system of the general hyperbolic differential equations of the third order with nonmultiple characteristics. The solution of this problem is constructed in an explicit form.
Aleksandr Anatol'evich Andreev, Juliya Olegovna Yakovleva   +1 more
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A uniqueness theorem for a goursat-type problem

Applied Mathematics Letters, 1992
Consider the problem (1) \(u_{tt}- \Delta u+ q(x)u=0\), \(x\in\mathbb{R}^ 3\), \(-r\leq t\leq r\), \(r=| x|\), (2) \(u=0\) at \(t=\pm r\), \[ \varliminf_{R\to\infty} \int_{| s|=R} \int_{-R}^ R | u_ r\mp u_ t|^ 2 dt ds=0.\tag{3} \] The boundary data are given on the characteristic cone \(t=\pm r\). Condition (3) is a condition at infinity. Assume that \(
Mishnaevskii, P.A., Ramm, A.G.
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Non-classic 3D Goursat Problem for One Hyperbolic Equation with Discontinuous Coefficients

Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2010
For a differential equation of hyperbolic type with discontinuous coefficients a 3D Goursat problem with nonclassical boundary conditions is considered, which requires no matching conditions.
I. G. Mamedov
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Generalized Solutions of a Periodic Goursat Problem [PDF]

Journal of Applied Analysis, 2001
Following, P. R. Garabedian (1964) and E. Goursat (1956) and the author's two papers (1995) and (1997), the Goursat problem in \(\mathbb{R}^2\) is \[ {\partial^2u\over\partial x \partial y} (x,y)= f(x,y,u(x, y));\;u(x,0)= v(x);\;u(0,y)= w(y), \] where \(f\) is a complex valued function on \(\mathbb{R}^2\times \mathbb{C}\), smooth in the four underlying
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