Dispersion and Asymptotic Profiles for Kirchhoff Equations
نویسنده
چکیده
The aim of this article is to describe asymptotic profiles for the Kirchhoff equation, and to establish time decay properties and dispersive estimates for Kirchhoff equations. For this purpose, the method of asymptotic integration is developed for the corresponding linear equations and representation formulae for their solutions are obtained. These formulae are analysed further to obtain the time decay rate of L–L norms of propagators for the corresponding Cauchy problems.
منابع مشابه
Asymptotic Integration and Dispersion for Hyperbolic Equations, with Applications to Kirchhoff Equations
The aim of this paper is to establish time decay properties and dispersive estimates for strictly hyperbolic equations with homogeneous symbols and with time-dependent coefficients whose derivatives belong to L(R). For this purpose, the method of asymptotic integration is developed for such equations and representation formulae for solutions are obtained. These formulae are analysed further to ...
متن کاملPositive solutions for asymptotically periodic Kirchhoff-type equations with critical growth
In this paper, we consider the following Kirchhoff-type equations: $-left(a+bint_{mathbb{R}^{3}}|nabla u|^{2}right)Delta u+V(x) u=lambda$ $f(x,u)+u^{5}, quad mbox{in }mathbb{R}^{3},$ $u(x)>0, quad mbox{in }mathbb{R}^{3},$ $uin H^{1}(mathbb{R}^{3}) ,$ where $a,b>0$ are constants and $lambda$ is a positive parameter. The aim of this paper is to study the existence of positive ...
متن کاملSemi-Analytical Solution for Vibration of Nonlocal Piezoelectric Kirchhoff Plates Resting on Viscoelastic Foundation
Semi-analytical solutions for vibration analysis of nonlocal piezoelectric Kirchhoff plates resting on viscoelastic foundation with arbitrary boundary conditions are derived by developing Galerkin strip distributed transfer function method. Based on the nonlocal elasticity theory for piezoelectric materials and Hamilton's principle, the governing equations of motion and boundary conditions are ...
متن کاملMODIFICATION OF THE OPTIMAL HOMOTOPY ASYMPTOTIC METHOD FOR LANE-EMDEN TYPE EQUATIONS
In this paper, modication of the optimal homotopy asymptotic method (MOHAM) is appliedupon singular initial value Lane-Emden type equations and results are compared with the available exactsolutions. The modied algorithm give the exact solution for dierential equations by using one iterationonly.
متن کاملDynamics of Vortices in Two-Dimensional Bose-einstein condensates
We derive the asymptotic motion equations of vortices for the time-dependent Gross–Pitaevskii equation with a harmonic trap potential. The asymptotic motion equations form a system of ordinary differential equations which can be regarded as a perturbation of the standard Kirchhoff problem. From the numerical simulation on the asymptotic motion equations, we observe that the bounded and collisio...
متن کامل