-
Energy methods for evolution problems.
-
Maximal monotone operators: basic properties, the Hille-Yosida theorem (the
selfadjoint case).
-
The heat equation: existence, uniqueness and regularity properties. The
maximum principle.
-
The wave equation: existence, uniqueness and regularity properties.
-
The Schrodinger equation: existence, uniqueness and regularity properties.
Bibliography
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V. Barbu, Partial Differential Equations and Boundary Value Problems,
Mathematics and its Applications, vol. 441, Kluwer, 1998.
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H. Brezis, Analyse fonctionnelle, Masson, Paris, 1992.
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H. Brezis, Master Course at the University of Paris 6, lecture notes, 1993.
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J. Jost, Partial Differential Equations, Springer Verlag, 2002.
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M. Renardy and R. Rogers, An Introduction to Partial Differential Equations,
Springer Verlag, 1996.