Search results for "Laplace"
showing 10 items of 227 documents
Laplace’s Method of Integration in the Path Integral Approach for the Probabilistic Response of Nonlinear Systems
2020
In this paper the response of nonlinear systems under stationary Gaussian white noise excitation is studied. The Path Integral (PI) approach, generally employed for evaluating the response Probability Density Function (PDF) of systems in short time steps based on the Chapman-Kolmogorov equation, is here used in conjunction with the Laplace’s method of integration. This yields an approximate analytical solution of the integral involved in the Chapman-Kolmogorov equation. Further, in this manner the repetitive integrations, generally required in the conventional numerical implementation of the procedure, can be circumvented. Application to a nonlinear system is considered, and pertinent compa…
Removable sets for continuous solutions of quasilinear elliptic equations
2001
We show that sets of n − p + α ( p − 1 ) n-p+\alpha (p-1) Hausdorff measure zero are removable for α \alpha -Hölder continuous solutions to quasilinear elliptic equations similar to the p p -Laplacian. The result is optimal. We also treat larger sets in terms of a growth condition. In particular, our results apply to quasiregular mappings.
Semilinear Robin problems driven by the Laplacian plus an indefinite potential
2019
We study a semilinear Robin problem driven by the Laplacian plus an indefinite potential. We consider the case where the reaction term f is a Carathéodory function exhibiting linear growth near ±∞. So, we establish the existence of at least two solutions, by using the Lyapunov-Schmidt reduction method together with variational tools.
Fractional differential equations solved by using Mellin transform
2014
In this paper, the solution of the multi-order differential equations, by using Mellin Transform, is proposed. It is shown that the problem related to the shift of the real part of the argument of the transformed function, arising when the Mellin integral operates on the fractional derivatives, may be overcame. Then, the solution may be found for any fractional differential equation involving multi-order fractional derivatives (or integrals). The solution is found in the Mellin domain, by solving a linear set of algebraic equations, whose inverse transform gives the solution of the fractional differential equation at hands.
Mellin transform approach for the solution of coupled systems of fractional differential equations
2015
In this paper, the solution of a multi-order, multi-degree-of-freedom fractional differential equation is addressed by using the Mellin integral transform. By taking advantage of a technique that relates the transformed function, in points of the complex plane differing in the value of their real part, the solution is found in the Mellin domain by solving a linear set of algebraic equations. The approximate solution of the differential (or integral) equation is restored, in the time domain, by using the inverse Mellin transform in its discretized form.
A fast hierarchical dual boundary element method for three-dimensional elastodynamic crack problems
2010
In this work a fast solver for large-scale three-dimensional elastodynamic crack problems is presented, implemented, and tested. The dual boundary element method in the Laplace transform domain is used for the accurate dynamic analysis of cracked bodies. The fast solution procedure is based on the use of hierarchical matrices for the representation of the collocation matrix for each computed value of the Laplace parameter. An ACA (adaptive cross approximation) algorithm is used for the population of the low rank blocks and its performance at varying Laplace parameters is investigated. A preconditioned GMRES is used for the solution of the resulting algebraic system of equations. The precond…
Online Edge Flow Imputation on Networks
2022
Author's accepted manuscript © 2022 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. An online algorithm for missing data imputation for networks with signals defined on the edges is presented. Leveraging the prior knowledge intrinsic to real-world networks, we propose a bi-level optimization scheme that exploits the causal dependencies and the flow conservation, respe…
On One Identification Problem in Linear Elasticity
1990
In practice we meet problems, when having the solution of partial differential equation, we want to discover parts in the domain of its definition where the solution has some specific properties. In [1] and [2] the problem of identification of a curve φ, lying inside of Ω such that the flux \(\int{_{\varphi }}\frac{\partial u}{\partial n}ds\) is maximal has been studied, where u is the solution of mixed—boundary value problem for Laplacian operator.
Response of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitations: A Path Integral approach based on La…
2023
In this paper, an approximate analytical technique is developed for determining the non-stationary response amplitude probability density function (PDF) of nonlinear/hysteretic oscillators endowed with fractional element and subjected to evolutionary excitations. This is achieved by a novel formulation of the Path Integral (PI) approach. Specifically, a stochastic averaging/linearization treatment of the original fractional order governing equation of motion yields a first-order stochastic differential equation (SDE) for the oscillator response amplitude. Associated with this first-order SDE is the Chapman–Kolmogorov (CK) equation governing the evolution in time of the non-stationary respon…
Parametric nonlinear singular Dirichlet problems
2019
Abstract We consider a nonlinear parametric Dirichlet problem driven by the p -Laplacian and a reaction which exhibits the competing effects of a singular term and of a resonant perturbation. Using variational methods together with suitable truncation and comparison techniques, we prove a bifurcation-type theorem describing the dependence on the parameter of the set of positive solutions.