Abstract
Identification problems for abstract semilinear parabolic evolution equations are studied. The problems are formulated by a minimization of quadratic cost functionals, and the existence and characterization problems are investigated. The existence of optimal parameters and necessary optimality conditions for the functionals are established by the continuity and Gateaux differentiability of solutions on parameters. An application to the semilinear diffusion equations with unknown spatially varying coefficients is given.
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