IJPAM: Volume 75, No. 1 (2012)
EQUATION WITH NEUMANN BOUNDARY CONDITIONS
Minot State University
Minot 58707, USA
Abstract. In this paper we study an identification problem for physical parameters associated with damped sine-Gordon equation with Neumann boundary conditions. The existence, uniqueness, and continuous dependence of weak solution of sine-Gordon equations are established. The method of transposition is used to prove the Gâteaux differentiability of the solution map. The Gâteaux differential of the solution map is characterized. The optimal parameters are established. Computational algorithm and numerical results are presented.
Received: November 14, 2011
AMS Subject Classification: 35B30, 49J50
Key Words and Phrases: identification problem, Neumann boundary conditions, Gâteaux differentiability, optimal parameters
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Source: International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395