Abstract
Some types of boundary optimal control problems governed by the nonlinear phase-field transition system, are introduced and analyzed in this Chapter.
The aim of Section 3.1 is to prove (for later use) a priori estimates in L2([0, T];H2( )) for unknown u, ' in phase-field system, in the presence of following boundary conditions (see (30), (300) in Preface):....
Keywords: Nonlinear parabolic systems, free boundary problems for PDE, inverse problems, necessary conditions for optimality, duality, abstract approximation theory, methods of approximations based on necessary conditions, stability and convergence of numerical methods, computer science, analysis of algorithms, methods of gradient type, phase transitions, applications in engineering and industry.
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