Continuous Dependence on Boundary Conditions

2016 ◽  
pp. 17-23
Author(s):  
Adam Bobrowski
Keyword(s):  
Boundary Conditions ◽  
Continuous Dependence

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>

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

Continuous dependence on the boundary conditions for the Wentzell Laplacian

2008 ◽  
Vol 77 (1) ◽  
pp. 101-108 ◽  
Author(s):  
Giuseppe Maria Coclite ◽  
Angelo Favini ◽  
Gisèle Ruiz Goldstein ◽  
Jerome A. Goldstein ◽  
Silvia Romanelli
Keyword(s):  
Boundary Conditions ◽  
Continuous Dependence ◽  
Wentzell Laplacian

scholarly journals k-component disconjugacy for systems of ordinary differential equations

1986 ◽  
Vol 9 (2) ◽  
pp. 373-380
Author(s):  
Johnny Henderson
Keyword(s):  
Differential Equations ◽  
Boundary Conditions ◽  
Ordinary Differential Equations ◽  
Continuous Dependence ◽  
Variational Equation ◽  
Order System ◽  
Differentiability Of Solutions

Disconjugacy of thekth component of themth order system ofnth order differenttal equationsY(n)=f(x,Y,Y′,…,Y(n−1)), (1.1), is defined, wheref(x,Y1,…,Yn),∂f∂yij(x,Y1,…,Yn):(a,b)×Rmn→Rmare continuous. Given a solutionY0(x)of (1.1),k-component disconjugacy of the variational equationZ(n)=∑i=1nfYi(x,Y0(x),…,Y0(n−1)(x))Z(i−1), (1.2), is also studied. Conditions are given for continuous dependence and differentiability of solutions of (1.1) with respect to boundary conditions, and then intervals on which (1.1) isk-component disconjugate are characterized in terms of intervals on which (1.2) isk-component disconjugate.

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