|Vorlesung 2 std.||Di 13:10-14:40||C209||1.3.|
Similarly, partial differential equations like the heat equation fit within this framework if the matrix A is replaced by the Laplace operator. However, since the Laplace operator is not bounded, the series for the exponential will not converge and this raises the question how the exponential should be defined in this case. Moreover, solutions of the heat equation exist in general only for positive times and the solution operator can form at best a semigroup.
Giving a solid mathematical foundation to this approach will be the aim of the present course.
- K.-J. Engel und R. Nagl, A Short Course on Operator Semigroups, Springer, New York, 2006.
- L. C. Evans, Partial Differential Equations, 2nd ed., Amer. Mat. Soc., Providence, 2010.
- J. A. Goldstein, Semigroups of Linear Operators and Applications, Oxford Univ. Press, Oxford, 1985.
- A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer, New York, 1983.