Random-field Solutions to Linear Hyperbolic Stochastic Partial Differential Equations with Variable Coefficients [PDF]
, 2017 In this article we show the existence of a random-field solution to linear stochastic partial differential equations whose partial differential operator is hyperbolic and has variable coefficients that may depend on the temporal and spatial argument. The
Ascanelli, Alessia, Süß, André
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Bäcklund Transformations for Liouville Equations with Exponential Nonlinearity
Axioms, 2021 This work aims to obtain new transformations and auto-Bäcklund transformations for generalized Liouville equations with exponential nonlinearity having a factor depending on the first derivatives.
Tatyana V. Redkina +3 more
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A similar for ∆1 problem for the second order hyperbolic equation in the 3D euclidean space
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2015 The second-order hyperbolic type equation is considered in the 3D Euclidean space. Boundary value problem is posed in the infinite cylindrical region bounded by the characteristic surfaces of this equation with data on the related characteristic surfaces ...
Irina N Rodionova +1 more
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Absorbing boundary conditions for second-order hyperbolic equations [PDF]
Journal of Computational Physics, 1990 A hierarchy of absorbing boundary conditions is derived for transonic small perturbation equations of unsteady flows. The application is demonstrated by numerical experiments. The results show the improved performance of second-order absorbing boundary conditions over first- order conditions.
Jiang, Hong, Wong, Yau Shu
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Numerical Evolution of Black Holes with a Hyperbolic Formulation of General Relativity [PDF]
, 1997 We describe a numerical code that solves Einstein's equations for a Schwarzschild black hole in spherical symmetry, using a hyperbolic formulation introduced by Choquet-Bruhat and York.
A. Abrahams +28 more
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The Goursat-type problem for a hyperbolic equation and system of third order hyperbolic equations
Vestnik Samarskogo Gosudarstvennogo Tehničeskogo Universiteta. Seriâ: Fiziko-Matematičeskie Nauki, 2019 In the first part of this study, the well-posed Goursat-type problem is considered for the hyperbolic differential equation of the third order with non-multiple characteristics.
Aleksandr Anatol'evich Andreev +1 more
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Hyperbolicity of second order in space systems of evolution equations [PDF]
Classical and Quantum Gravity, 2006 A possible definition of strong/symmetric hyperbolicity for a second-order system of evolution equations is that it admits a reduction to first order which is strongly/symmetric hyperbolic. We investigate the general system that admits a reduction to first order and give necessary and sufficient criteria for strong/symmetric hyperbolicity of the ...
Gundlach, Carsten +1 more
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Hyperbolic Second Order Equations with Non-Regular Time Dependent Coefficients [PDF]
Archive for Rational Mechanics and Analysis, 2014 In this paper we study weakly hyperbolic second order equations with time dependent irregular coefficients. This means to assume that the coefficients are less regular than H lder. The characteristic roots are also allowed to have multiplicities. For such equations, we describe the notion of a `very weak solution' adapted to the type of solutions that
Ruzhansky, M, Garetto, C
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On the Green functions of gravitational radiation theory [PDF]
, 2001 Previous work in the literature has studied gravitational radiation in black-hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables,
Esposito, Giampiero
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Path Integral Solution of Linear Second Order Partial Differential Equations I. The General Construction [PDF]
, 2004 A path integral is presented that solves a general class of linear second order partial differential equations with Dirichlet/Neumann boundary conditions. Elementary kernels are constructed for both Dirichlet and Neumann boundary conditions.
Abraham +16 more
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