The Notion of Energy of Solutions: One of the Most Important Quantities

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

Chapter Chapter 11 in Methods for Partial Differential Equations, 2018, pp 147-170 from Springer

Abstract: Abstract The main issue of this chapter is the notion of energy of solutions, a very effective tool for the treatment of nonstationary or evolution models. We introduce energies for different models and explain conservation of energies, if possible. Sometimes, the choice of a suitable energy seems to be a miracle, sometimes one has different choices. Do we have energy conservation? Do we have blow up of the energy for t →∞? Do we have a decay of the energy for t →∞? These and related questions will be answered in this chapter. Moreover, it is shown how lower order terms may influence the choice and the long-time behavior of a suitable energy. Here we restrict ourselves to mass and different damping terms. Finally, we explain for several models the long-time behavior of local energies for solutions of mixed problems with Dirichlet condition in exterior domains.

Keywords: Exterior Domain; Mixed Problem; Damping Term; Sobolev Solutions; Local Energy Decay Estimate (search for similar items in EconPapers)
Date: 2018
References: Add references at CitEc
Citations:

There are no downloads for this item, see the EconPapers FAQ for hints about obtaining it.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-319-66456-9_11

Ordering information: This item can be ordered from
http://www.springer.com/9783319664569

DOI: 10.1007/978-3-319-66456-9_11

Access Statistics for this chapter

More chapters in Springer Books from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().