Partial Differential Inclusions

Michał Kisielewicz
Additional contact information
Michał Kisielewicz: University of Zielona Góra

Chapter Chapter 6 in Stochastic Differential Inclusions and Applications, 2013, pp 217-252 from Springer

Abstract: Abstract The present chapter is devoted to partial differential inclusions described by the semielliptic set-valued partial differential operators $$\mathbb{L}_{FG}$$ generated by given set-valued mappings F and G. Such inclusions will be investigated by stochastic methods. As in the theory of ordinary differential inclusions, the existence of solutions of such inclusions follows from continuous selections theorems and existence theorems for partial differential equations. Therefore, Sects. 2 and 3 are devoted to existence and representation theorems for elliptic and parabolic partial differential equations. Some selection theorems and existence and representation theorems for such partial differential inclusions follow. It will be proved that solutions of initial and boundary value problems for partial differential inclusions can be described by weak solutions of stochastic functional inclusions SFI(F, G), as considered in Chap. 4.

Keywords: Partial Differential Inclusions; Parabolic Partial Differential Equations; Weak Solution; Continuous Selector; Dirichlet-Poisson Problem (search for similar items in EconPapers)
Date: 2013
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:spochp:978-1-4614-6756-4_6

Ordering information: This item can be ordered from
http://www.springer.com/9781461467564

DOI: 10.1007/978-1-4614-6756-4_6

Access Statistics for this chapter

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