Results 121 to 130 of about 179,434,279 (151)

Asymptotics of the solutions of integral equations with a difference kernel

Ukrainian Mathematical Journal, 1982
\textit{S. Karlin} [Pac. J. Math. 5, 229-257 (1955; Zbl 0067.349)] considered equations of the form \[ (1)\quad u(\xi)-\int^{\infty}_{- \infty}u(\xi -t)dF(t)=g(\xi),\quad ...
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UNIFORMLY ASYMPTOTIC SOLUTIONS FOR PSEUDODIFFERENTIAL EQUATIONS WITH SINGULAR INTEGRAL OPERATORS

Journal of Computational Acoustics, 2001
Uniformly asymptotic frequency-domain solutions for a class of hyperbolic equations with singular convolution operators are derived. Asymptotic solutions for this class of equations involve additional parameters — called attenuation parameters — which control the smoothing of the wavefield at the wavefront.
Hanyga, A., Seredyńska, M.
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On the asymptotic solution of a nonlinear Volterra integral equation

Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences, 1971
Abstract A technique based on the analytic continuation and study of the pole diagram of the Mellin transform has been described for obtaining asymptotic solution of nonlinear Volterra type integral equations for small and large values of the argument.
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Asymptotic Behavior of the Solution of the Integral Transport Equation in Slab Geometry

SIAM Journal on Applied Mathematics, 1977
We study the continuity and differentiability properties of the solution $\varphi $ of a linear integral equation arising in transport theory. The integral equation is described by an operator T which maps bounded functions into Holder continuous functions. T does not commute with the differential operator D.
Kaper, Hans G., Kellogg, R. Bruce
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Asymptotic expansion of the solutions of integral equations with δ-form kernels

USSR Computational Mathematics and Mathematical Physics, 1972
Abstract WE consider the problem of constructing asymptotic expansions of the solutions of integral equations of the second kind depending on a small parameter ϵ 〉 0 in such a way that as ϵ 〉 0 the kernel of the integral operator has the nature of a δ-function.
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ASYMPTOTIC BEHAVIOR OF THE SOLUTION OF A SINGULAR INTEGRAL EQUATION WITH A SMALL PARAMETER

Mathematics of the USSR-Sbornik, 1976
We construct an asymptotic expansion as that is uniform in of the solution of the singular integral equation Bibliography: 3 titles.
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Asymptotic Integration of the Principal Solution of a Second-Order Differential Equation

Bulletin of the London Mathematical Society, 1991
The second-order linear differential equation \((r(t)x')'+(f(t)+q(t))x=0\) is considered as a perturbation of the equation \((r(t)y')'+f(t)y=0\), where \(r,f,q,x\) and \(y\) are continuous real-valued and \(r>0\). It is known that if the unperturbed equation is nonoscillatory it has a unique principal solution \(y_ 1\) (up to a constant factor) such ...
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On the asymptotic behaviour of solutions of nonlinear integral equations in BANACH spaces

Mathematische Nachrichten, 1979
AbstractThe asymptotic behaviour of solutions of nonlinear VOLTERRA integral equations is studied in a real BANACH spaces. The nonlinear operator is assumed to satisfy some accretivity‐type conditions.
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On the Asymptotic Behavior of Finite Energy Solutions of an Abstract Integral Equation

SIAM Journal on Mathematical Analysis, 1978
We define an energy function for a solution of the abstract nonlinear integral equation \[x'(t) + \partial \varphi (x(t)) + \int_0^t {a(t - s)\partial \psi (x(s))ds \ni f(t)} \quad (t \in R^ + ),\] and study the asymptotic behavior of the solutions for which the energy function is bounded. We also investigate the problem of getting an a priori bound on
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Higher-dimensional nonlinear integrable equations: Asymptotics of solutions and perturbations

Journal of Mathematical Sciences, 2005
The survey is devoted to the analysis of solutions of (2+1)D integrable equations -- Kadomtsev-Petviashvili, Davey-Stewartson, Ishimori ones. Using the inverse scattering transform method the author studies temporal asymptotics of decreasing solutions and formal asymptotic solutions for perturbations of solutions to Davey-Stewartson equations.
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