scholarly journals An Existence Theorem for General Control Problems of Nonlinear Evolution Equations of First Order

1990 ◽  
Vol 9 (2) ◽  
pp. 113-120
Author(s):  
Bernd Krause
Keyword(s):  
Existence Theorem ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Control Problems ◽  
General Control ◽  
First Order

A METHOD TO CONSTRUCT WEIERSTRASS ELLIPTIC FUNCTION SOLUTION FOR NONLINEAR EQUATIONS

2011 ◽  
Vol 25 (14) ◽  
pp. 1931-1939 ◽  
Author(s):  
LIANG-MA SHI ◽  
LING-FENG ZHANG ◽  
HAO MENG ◽  
HONG-WEI ZHAO ◽  
SHI-PING ZHOU
Keyword(s):  
Nonlinear Equations ◽  
Elliptic Function ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Evolution Equations ◽  
Order Derivative ◽  
First Order ◽  
Function Solution ◽  
Weierstrass Elliptic Function ◽  
Klein Gordon

A method for constructing the solutions of nonlinear evolution equations by using the Weierstrass elliptic function and its first-order derivative was presented. This technique was then applied to Burgers and Klein–Gordon equations which showed its efficiency and validality for exactly some solving nonlinear evolution equations.

scholarly journals Analysis of a frictionless contact problem for elastic-viscoplastic materials

2012 ◽  
Vol 17 (1) ◽  
pp. 99-117
Author(s):  
Mohamed Selmani ◽  
Lynda Selmani
Keyword(s):  
Contact Problem ◽  
Existence And Uniqueness ◽  
Evolution Equations ◽  
Order Differential Equation ◽  
Nonlinear Evolution ◽  
Monotone Operators ◽  
Uniqueness Result ◽  
Nonlinear Evolution Equations ◽  
Frictionless Contact ◽  
First Order

We consider a dynamic frictionless contact problem for elastic-viscoplastic materials with damage. The contact is modelled with normal compliance condition. The adhesion of the contact surfaces is considered and is modelled with a surface variable, the bonding field whose evolution is described by a first order differential equation. We derive variational formulation for the model and prove an existence and uniqueness result of the weak solution. The proof is based on arguments of nonlinear evolution equations with monotone operators, a classical existence and uniqueness result on parabolic inequalities, differential equations and fixed-point arguments.

scholarly journals Optimality conditions for systems driven by nonlinear evolution equations

1995 ◽  
Vol 1 (1) ◽  
pp. 27-36
Author(s):  
N. Papageorgiou
Keyword(s):  
Nonlinear Evolution Equation ◽  
Evolution Equations ◽  
Optimal Control Problems ◽  
Nonlinear Evolution ◽  
Sufficient Conditions ◽  
Nonlinear Evolution Equations ◽  
Control Problems ◽  
Terminal Constraints ◽  
Sufficient Conditions For Optimality ◽  
Necessary And Sufficient

Using the Dubovitskii-Milyutin theory we derive necessary and sufficient conditions for optimality for a class of Lagrange optimal control problems monitored by a nonlinear evolution equation and involving initial and/or terminal constraints. An example of a parabolic control system is also included.

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