CONTINUOUS DEPENDENCE OF THE SOLUTIONS OF ELUPTIC BWNOARY VALUE PROBLEMS ON THE COEFFICIENTS, RIGHT HAND SIDES AND BOUNDARY CONDITIONS

1981 ◽  
Vol 4 (3) ◽  
pp. 167-183 ◽  
Author(s):  
B Kok ◽  
F D Penning
Keyword(s):  
Boundary Conditions ◽  
Continuous Dependence ◽  
Right Hand

On Fourier Series in Eigenfunctions of Elliptic Boundary Value Problems

2003 ◽  
Vol 10 (3) ◽  
pp. 401-410
Author(s):  
M. S. Agranovich ◽  
B. A. Amosov
Keyword(s):  
Fourier Series ◽  
Boundary Conditions ◽  
Fourier Coefficients ◽  
Elliptic Boundary ◽  
A Priori ◽  
Adjoint Problem ◽  
Elliptic Boundary Value ◽  
Right Hand ◽  
The Difference ◽  
The Right

Abstract We consider a general elliptic formally self-adjoint problem in a bounded domain with homogeneous boundary conditions under the assumption that the boundary and coefficients are infinitely smooth. The operator in 𝐿2(Ω) corresponding to this problem has an orthonormal basis {𝑢𝑙} of eigenfunctions, which are infinitely smooth in . However, the system {𝑢𝑙} is not a basis in Sobolev spaces 𝐻𝑡 (Ω) of high order. We note and discuss the following possibility: for an arbitrarily large 𝑡, for each function 𝑢 ∈ 𝐻𝑡 (Ω) one can explicitly construct a function 𝑢0 ∈ 𝐻𝑡 (Ω) such that the Fourier series of the difference 𝑢 – 𝑢0 in the functions 𝑢𝑙 converges to this difference in 𝐻𝑡 (Ω). Moreover, the function 𝑢(𝑥) is viewed as a solution of the corresponding nonhomogeneous elliptic problem and is not assumed to be known a priori; only the right-hand sides of the elliptic equation and the boundary conditions for 𝑢 are assumed to be given. These data are also sufficient for the computation of the Fourier coefficients of 𝑢 – 𝑢0. The function 𝑢0 is obtained by applying some linear operator to these right-hand sides.

scholarly journals Continuous dependence and optimal control of a dynamic elastic-viscoplastic contact problem with non-monotone boundary conditions

2022 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Xilu Wang ◽  
Xiaoliang Cheng
Keyword(s):  
Optimal Control ◽  
Boundary Conditions ◽  
Continuous Dependence ◽  
Initial Conditions ◽  
Weak Form ◽  
Constitutive Law ◽  
Optimal Solutions ◽  
Existence Of Optimal Solutions ◽  
External Forces ◽  
Weak Topologies

<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>

Continuous dependence of a solution of a neutral functional differential equation on the right-hand side and initial data taking into account perturbations of variable delays

2016 ◽  
Vol 23 (4) ◽  
pp. 519-535
Author(s):  
Nika Gorgodze ◽  
Ia Ramishvili ◽  
Tamaz Tadumadze
Keyword(s):  
Initial Data ◽  
Continuous Dependence ◽  
Functional Differential Equations ◽  
Initial Vector ◽  
Initial Moment ◽  
Neutral Functional Differential Equations ◽  
Variable Delays ◽  
Right Hand ◽  
Functional Differential ◽  
The Right

AbstractTheorems on the continuous dependence of a solution of the Cauchy problem with respect to the nonlinear term of the right-hand side and initial data are proved for neutral functional differential equations whose right-hand sides are linear with respect to the prehistory of the phase velocity. Under the initial data we imply a collection of initial moment, variable delays entering in the phase coordinates, initial vector and initial functions. In this paper, an essential novelty is that perturbations of variable delays are taken into account in proving the main theorems.

scholarly journals Continuous dependence in hyperbolic problems with Wentzell boundary conditions

2014 ◽  
Vol 13 (1) ◽  
pp. 419-433 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
◽  
Angelo Favini ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Continuous Dependence ◽  
Hyperbolic Problems ◽  
Wentzell Boundary Conditions
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