A convolution integral equation solved by Laplace transformations
نویسندگان
چکیده
منابع مشابه
A Certain Integral-recurrence Equation with Discrete-continuous Auto-convolution
Laplace transform and some of the author’s previous results about first order differential-recurrence equations with discrete auto-convolution are used to solve a new type of non-linear quadratic integral equation. This paper continues the author’s work from other articles in which are considered and solved new types of algebraic-differential or integral equations.
متن کاملTransmission problem for the Laplace equation and the integral equation method
We shall study a weak solution in the Sobolev space of the transmission problem for the Laplace equation using the integral equation method. First we use the indirect integral equation method. We look for a solution in the form of the sum of the double layer potential corresponding to the skip of traces on the interface and a single layer potential with an unknown density. We get an integral eq...
متن کاملA Generalized Convolution for Finite Fourier Transformations
Presented to the Society, April 16, 1948; received by the editors June 25, 1948. 1 The author wishes to thank Professor R. V. Churchill for his advice in the preparation of this paper. The content of this paper is part of a dissertation submitted in partial fulfillment of the requirements for the degree of doctor of philosophy in the University of Michigan. 2 The numbers in brackets refer to th...
متن کاملOn Laplace ' S Integral Equations
which is known in the literature as Laplace's integral equation. The contour (C) and the function f(z) are supposed given and F(x) is to be found. In the case when the contour (C) consists of the positive part of the axis of reals, the solution of the equation (*■) was given by H. Poincaré t and H. Hamburger. % Each of these authors considers F(x) as a function of the real variable *. When the ...
متن کاملThe Laplace Equation
Definition 1. Among the most important and ubiquitous of all partial differential equations is Laplace’s Equation: ∆u = 0, where the Laplacian operator ∆ acts on the function u : U → R (U is open in R) by taking the sum of the unmixed partial derivatives. For example: n = 1: ∆u = ∂ 2u ∂x2 = u = 0 In this simple case, the solution u = ax + b is found by integrating twice. n = 2: ∆u = ∂ 2u ∂x1 + ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Computational and Applied Mathematics
سال: 1985
ISSN: 0377-0427
DOI: 10.1016/0377-0427(85)90052-4