Phase Space Analysis and Smoothing for Schrödinger Equations

Marcelo R. Ebert and Michael Reissig
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Marcelo R. Ebert: University of São Paulo, Department of Computing and Mathematics
Michael Reissig: TU Bergakademie Freiberg, Institute of Applied Analysis

Chapter Chapter 13 in Methods for Partial Differential Equations, 2018, pp 181-189 from Springer

Abstract: Abstract Consider this chapter as a brief introduction to some properties of solutions to the classical Schrödinger equation with or without mass term. We continue the discussion of L p − L q estimates for this special example of a dispersive equation. In particular, we explain differences between expected results for the Schrödinger equation and for those the heat equation. In addition to these applications of phase space analysis we discuss the topic “Smoothing effect” for solutions, local and global smoothing as well.

Keywords: Phase Space Analysis; Global Smoothing; Heat Equation; Conjugate Lines; Local Smoothing Properties (search for similar items in EconPapers)
Date: 2018
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-66456-9_13

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DOI: 10.1007/978-3-319-66456-9_13

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