Search results for " integral equation."
showing 10 items of 63 documents
A note on the uniqueness and attractive behavior of solutions for nonlinear Volterra equations
2001
In this paper we prove that positive solutions of some nonlinear Volterra integral equations must be locally bounded and global attractors of positive functions. These results complete previous results about the existence and uniqueness of solutions and their attractive behavior.
Schaefer–Krasnoselskii fixed point theorems using a usual measure of weak noncompactness
2012
Abstract We present some extension of a well-known fixed point theorem due to Burton and Kirk [T.A. Burton, C. Kirk, A fixed point theorem of Krasnoselskii–Schaefer type, Math. Nachr. 189 (1998) 423–431] for the sum of two nonlinear operators one of them compact and the other one a strict contraction. The novelty of our results is that the involved operators need not to be weakly continuous. Finally, an example is given to illustrate our results.
Blow-up collocation solutions of nonlinear homogeneous Volterra integral equations
2011
In this paper, collocation methods are used for detecting blow-up solutions of nonlinear homogeneous Volterra-Hammerstein integral equations. To do this, we introduce the concept of "blow-up collocation solution" and analyze numerically some blow-up time estimates using collocation methods in particular examples where previous results about existence and uniqueness can be applied. Finally, we discuss the relationships between necessary conditions for blow-up of collocation solutions and exact solutions.
Hollow system with fin. Transient Green function method combination for two hollow cylinders
2017
In this paper we develop mathematical model for three dimensional heat equation for the system with hollow wall and fin and construct its analytical solution for two hollow cylindrical sample. The method of solution is based on Green function method for one hollow cylinder. On the conjugation conditions between both hollow cylinders we construct solution for system wall with fin. As result we come to integral equation on the surface between both hollow cylinders. Solution is obtained in the form of second kind Fredholm integral equation. The generalizing of Green function method allows us to use Green function method for regular non-canonical domains.
Quadrature rules for qualocation
2003
Qualocation is a method for the numerical treatment of boundary integral equations on smooth curves which was developed by Chandler, Sloan and Wendland (1988-2000) [1,2]. They showed that the method needs symmetric J–point–quadrature rules on [0, 1] that are exact for a maximum number of 1–periodic functions The existence of 2–point–rules of that type was proven by Chandler and Sloan. For J ∈ {3, 4} such formulas have been calculated numerically in [2]. We show that the functions Gα form a Chebyshev–system on [0, 1/2] for arbitrary indices a and thus prove the existence of such quadrature rules for any J.
A simulation model for electromagnetic transients in lightning protection systems
2002
This paper deals with the evaluation of electromagnetic transients in a lightning protection system (LPS). A field approach is used, based on the numerical solution of a modified version of the thin-wire electric field integral equation in the frequency domain. Time profiles of interesting electromagnetic quantities are computed by using a discrete fast Fourier transform algorithm. The model takes into account coupling effects among aerial parts and ground electrodes in order to correctly estimate the quantities which can determine electromagnetic hazard inside the LPS; transient touch and step voltages can be easily evaluated also taking into account the human body presence on the soil sur…
Non-Lipschitz Homogeneous Volterra Integral Equations
2018
In this chapter we introduce a class of nonlinear Volterra integral equations (VIEs) which have certain properties that deviate from the standard results in the field of integral equations. Such equations arise from various problems in shock wave propagation with nonlinear flux conditions. The basic equation we will consider is the nonlinear homogeneous Hammerstein–Volterra integral equation of convolution type $$\displaystyle u(t) = \int _0^t k(t-s) g(u(s))\,\mathrm {d}s. $$ When g(0) = 0, this equation has function u ≡ 0 as a solution (trivial solution). It is interesting to determine whether there exists a nontrivial solution or not. Classical results on integral equations are not to be …
Some coincidence and periodic points results in a metric space endowed with a graph and applications
2015
The purpose of this paper is to obtain some coincidence and periodic points results for generalized $F$-type contractions in a metric space endowed with a graph. Some examples are given to illustrate the new theory. Then, we apply our results to establishing the existence of solution for a certain type of nonlinear integral equation.
Boundary Element Method for Composite Laminates
2017
The boundary element method (BEM) is a numerical technique to solve engineering/physical problems formulated in terms of boundary integral equations. Composite laminates are assemblages of stacked different materials layers, generally consisting of variously oriented fibrous composite materials
Reconstruction from boundary measurements for less regular conductivities
2012
In this paper, following Nachman's idea and Haberman and Tataru's idea, we reconstruct $C^1$ conductivity $\gamma$ or Lipchitz conductivity $\gamma$ with small enough value of $|\nabla log\gamma|$ in a Lipschitz domain $\Omega$ from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$. In the appendix the authors and R. M. Brown recover the gradient of a $C^1$-conductivity at the boundary of a Lipschitz domain from the Dirichlet-to-Neumann map $\Lambda_{\gamma}$.