ISSN:
1573-2878
Keywords:
Nonlinear parabolic equations
;
functional analysis
;
existence
;
uniqueness
;
control problems
;
Newton's method
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The solution of a nonlinear parabolic equation is studied from both the functional and the numerical points of view. Existence, uniqueness, and stability results are given. A boundary-control problem is then presented. Expressions of the gradient and the Hessian of the cost function are given with some details, and the Newton method is compared with a gradient method and the Fletcher-Reeves method. Numerical results are given. The paper concludes with a discussion of the advantages of the Newton method as applied to a control problem.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00939935
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