# continuous dependenceRecently Published Documents

722
(FIVE YEARS 107)

## H-INDEX

31
(FIVE YEARS 2)

2022 ◽
Vol 10 (2) ◽
pp. 245
Author(s):
Ahmed M. A. El-Sayed ◽
Yasmin M. Y. Omar

Differential and integral equations in reflexive Banach spaces have gained great attention and hve been investigated in many studies and monographs. Inspired by those, we study the existence of the solution to a delay functional integral equation of Volterra-Stieltjes type and its corresponding delay-functional integro-differential equation in reflexive Banach space E. Sufficient conditions for the uniqueness of the solutions are given. The continuous dependence of the solutions on the delay function, the initial data, and some others parameters are proved.

2022 ◽
Vol 0 (0) ◽
pp. 0
Author(s):
Xilu Wang ◽
Xiaoliang Cheng
Keyword(s):

<p style='text-indent:20px;'>In this paper, we consider continuous dependence and optimal control of a dynamic elastic-viscoplastic contact model with Clarke subdifferential boundary conditions. Since the constitutive law of elastic-viscoplastic materials has an implicit expression of the stress field, the weak form of the model is an evolutionary hemivariational inequality coupled with an integral equation. By providing some equivalent weak formulations, we prove the continuous dependence of the solution on external forces and initial conditions in the weak topologies. Finally, the existence of optimal solutions to a boundary optimal control problem is established.</p>

2021 ◽
pp. 1-26
Author(s):
Tianfang Wang ◽
Wen Zhang ◽
Jian Zhang
Keyword(s):

In this paper we study the Dirac equation with Coulomb potential − i α · ∇ u + a β u − μ | x | u = f ( x , | u | ) u , x ∈ R 3 where a is a positive constant, μ is a positive parameter, α = ( α 1 , α 2 , α 3 ), α i and β are 4 × 4 Pauli–Dirac matrices. The Dirac operator is unbounded from below and above so the associate energy functional is strongly indefinite. Under some suitable conditions, we prove that the problem possesses a ground state solution which is exponentially decay, and the least energy has continuous dependence about μ. Moreover, we are able to obtain the asymptotic property of ground state solution as μ → 0 + , this result can characterize some relationship of the above problem between μ > 0 and μ = 0.

2021 ◽
Vol 9 (24) ◽
pp. 3234
Author(s):
Ahmed M. A. El-Sayed ◽
Hind H. G. Hashem ◽
Shorouk M. Al-Issa
Keyword(s):

In this work, we are discussing the solvability of an implicit hybrid delay nonlinear functional integral equation. We prove the existence of integrable solutions by using the well known technique of measure of noncompactnes. Next, we give the sufficient conditions of the uniqueness of the solution and continuous dependence of the solution on the delay function and on some functions. Finally, we present some examples to illustrate our results.

2021 ◽
Vol 0 (0) ◽
Author(s):
Nguyen Huy Tuan ◽
Daniel Lesnic ◽
Tran Ngoc Thach ◽
Tran Bao Ngoc
Keyword(s):

Abstract In this paper, we study the backward problem for the stochastic parabolic heat equation driven by a Wiener process. We show that the problem is ill-posed by violating the continuous dependence on the input data. In order to restore stability, we apply a filter regularization method which is completely new in the stochastic setting. Convergence rates are established under different a priori assumptions on the sought solution.

2021 ◽
Vol 4 ◽
pp. 100110
Author(s):
D.D. Pawar
Keyword(s):

Author(s):
Brian Straughan
Keyword(s):

AbstractIt is shown that the solution to the boundary - initial value problem for a Kelvin–Voigt fluid of order one depends continuously upon the Kelvin–Voigt parameters, the viscosity, and the viscoelastic coefficients. Convergence of a solution is also shown.

2021 ◽
Vol 24 (6) ◽
pp. 1758-1776
Author(s):
Xuping Zhang ◽
Pengyu Chen ◽
Donal O’Regan
Keyword(s):

Abstract In this article, we are concerned with the VIP of fractional fuzzy evolution equations in the space of triangular fuzzy numbers. The continuous dependence of two kinds of fuzzy mild solutions on initial values and orders for the studied problem is obtained. The results obtained in this paper improve and extend some related conclusions on this topic.

2021 ◽
Vol 2021 (1) ◽
Author(s):
Huanting Li ◽
Xiankang Chen
Keyword(s):

AbstractIn this paper, the dynamic behavior of a class of switched systems with internally forced switching (IFS) is investigated. By introducing the definitions of continuous dependence and differentiability, the continuous dependence and differentiability of the solution relative to the control function are obtained. In the past studies, the optimal control problem given by IFS mainly focused on a special class of controlled systems (the piece affine system). Our results lay a good foundation for studying the more general internally forced switching problem.

2021 ◽
Vol 5 (4) ◽
pp. 201
Author(s):
Ahmed M. A. El-Sayed ◽