Well-Posed Initial-Value Problems; Semigroups
Part of the Texts and Monographs in Physics book series (TMP)
This chapter gives the general theory of linear initial-value problems or problems of evolution in physics.
KeywordsBanach-space formulation strict solution Hadamard’s concept of a well-posed problem existence and uniqueness of the solution continuous dependence on the initial state generalized solution semigroup strongly continuous semigroup infinitesimal generator Hille-Yosida theorem inhomogeneous problems inhomogeneous boundary conditions problems with explicit time dependence applications to heat flow, wave motion, quantum mechanics, electromagnetism, and neutron transport
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