Abstract
Parameter identification problems of spatially varying coefficients in a class of strongly damped nonlinear wave equations are studied. The problems are formulated by a minimization of quadratic cost functionals by means of distributive and terminal values measurements. The existence of optimal parameters and necessary optimality conditions for the functionals are proved by the continuity and Gateaux differentiability of solutions on parameters. 1 Introduction Let Ω be an open bounded set of R n with the smooth boundary Γ. The inner product of R n is denoted by x · y for x, y ∈ R n . We put Q =( 0 ,T ) × Ω, Σ = (0 ,T ) × Γ for T> 0. We consider the following Dirichlet boundary value problem for the system of strongly damped nonlinear wave equations described by
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