Abstract
The results obtained for the modeling examples of Chapters 2–4 can be embedded in a general mathematical setting involving parabolic diffusion–convection–reaction systems (Chapters 2 and 3) or so–called biharmonic Petrowski systems (Chapter 4) defined on bounded higher–dimensional domains. This enables a rigorous formulation of the subsequently analyzed control problems.
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References
Evans, L.: Partial Differential Equations, Graduate Studies in Mathematics, vol. 19. American Mathematical Society, Rhode Island (2002)
Friedman, A.: Partial differential equations of parabolic type. Prentice–Hall, Englewood Cliffs (NJ) (1964)
Ladyženskaja, O., Solonnikov, V., Ural’ceva, N.: Linear and Quasi–linear Equations of Parabolic Type. Translations of Mathematical Monographs, 5th edn., vol. 23. American Mathematical Society, Rhode Island (1998)
Lions, J., Magenes, E.: Non–Homogeneous Boundary Value Problems and Applications, vol. 3. Springer, Berlin (1973)
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Meurer, T. (2013). Mathematical Problem Formulation. In: Control of Higher–Dimensional PDEs. Communications and Control Engineering. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30015-8_5
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DOI: https://doi.org/10.1007/978-3-642-30015-8_5
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