Approximate controllability of semilinear impulsive strongly damped wave equation

2015 ◽  
Vol 21 (1) ◽  
Author(s):  
Hanzel Larez ◽  
Hugo Leiva ◽  
Jorge Rebaza ◽  
Addison Ríos
Keyword(s):  
Fixed Point ◽  
Wave Equation ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Approximate Controllability ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

AbstractRothe's fixed-point theorem is applied to prove the interior approximate controllability of a semilinear impulsive strongly damped wave equation with Dirichlet boundary conditions in the space

scholarly journals An Existence Theorem for Fractional Hybrid Differential Inclusions of Hadamard Type with Dirichlet Boundary Conditions

2014 ◽  
Vol 2014 ◽  
pp. 1-7 ◽  
Author(s):  
Bashir Ahmad ◽  
Sotiris K. Ntouyas
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Existence Theorem ◽  
Point Theorem ◽  
Differential Inclusions ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions

This paper studies the existence of solutions for a boundary value problem of nonlinear fractional hybrid differential inclusions by using a fixed point theorem due to Dhage (2006). The main result is illustrated with the aid of an example.

scholarly journals On a singular sublinear polyharmonic problem

2006 ◽  
Vol 2006 ◽  
pp. 1-14 ◽  
Author(s):  
Sonia Ben Othman
Keyword(s):  
Fixed Point ◽  
Green Function ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Unit Ball ◽  
Existence Result ◽  
Dirichlet Boundary ◽  
Dirichlet Boundary Conditions ◽  
Combined Effects ◽  
Polyharmonic Equations

This paper deals with a class of singular nonlinear polyharmonic equations on the unit ballBinℝn (n≥2)where the combined effects of a singular and a sublinear term allow us by using the Schauder fixed point theorem to establish an existence result for the following problem:(−Δ)mu=φ(⋅,u)+ψ(⋅,u)inB(in the sense of distributions),u>0,lim⁡|x|→1u(x)/(1−|x|)m−1=0. Our approach is based on estimates for the polyharmonic Green function onBwith zero Dirichlet boundary conditions.

scholarly journals Existence of Solutions of a Nonlocal Elliptic System via Galerkin Method

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Alberto Cabada ◽  
Francisco Julio S. A. Corrêa
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Conditions ◽  
Galerkin Method ◽  
Positive Solution ◽  
Dirichlet Boundary ◽  
Existence Of Solutions ◽  
Dirichlet Boundary Conditions ◽  
Dimensional System ◽  
The Galerkin Method

By means of the Galerkin method and by using a suitable version of the Brouwer fixed-point theorem, we establish the existence of at least one positive solution of a nonlocal ellipticN-dimensional system coupled with Dirichlet boundary conditions.

scholarly journals On the strongly damped wave equation and the heat equation with mixed boundary conditions

2000 ◽  
Vol 5 (3) ◽  
pp. 175-189
Author(s):  
Aloisio F. Neves
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Heat Equation ◽  
Mixed Boundary ◽  
Strong Solutions ◽  
Mixed Boundary Conditions ◽  
Global Attractors ◽  
Damped Wave Equation ◽  
Strongly Damped Wave Equation ◽  
Strongly Damped

We study two one-dimensional equations: the strongly damped wave equation and the heat equation, both with mixed boundary conditions. We prove the existence of global strong solutions and the existence of compact global attractors for these equations in two different spaces.

scholarly journals Robustness of the controllability for the strongly damped wave equation under the influence of impulses, delays and nonlocal conditions

2019 ◽  
Vol 44 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Hugo Leiva
Keyword(s):  
Wave Equation ◽  
Approximate Controllability ◽  
Nonlocal Conditions ◽  
Time Interval ◽  
Short Time Interval ◽  
Damped Wave Equation ◽  
Qualitative Properties ◽  
Strongly Damped Wave Equation ◽  
Fixed Curve ◽  
Strongly Damped

This work proves the following conjecture: impulses, delays, and nonlocal conditions, under some assumptions, do not destroy some posed system qualitative properties since they are themselves intrinsic to it. we verified that the property of controllability is robust under this type of disturbances for the strongly damped wave equation. Specifically, we prove that the interior approximate controllability of linear strongly damped wave equation is not destroyed if we add impulses, nonlocal conditions and a nonlinear perturbation with delay in state. This is done by using new techniques avoiding fixed point theorems employed by A.E. Bashirov et al. In this case the delay help us to prove the approximate controllability of this system by pulling back the control solution to a fixed curve in a short time interval, and from this position, we are able to reach a neighborhood of the final state in time t by using that the corresponding linear strongly damped wave equation is approximately controllable on any interval {t0,T}, 0 < t0 < T.

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