Encyclopedia of Systems Biology

2013 Edition
| Editors: Werner Dubitzky, Olaf Wolkenhauer, Kwang-Hyun Cho, Hiroki Yokota

Partial Differential Equations, Poisson Equation

  • Brian D. Sleeman
Reference work entry
DOI: https://doi.org/10.1007/978-1-4419-9863-7_274

Synonyms

Definition

Poisson’s equation in two-dimensional space is the partial differential equation, to be solved for the function u, of the form
$$ \Delta u = f(x,y), $$
This is a preview of subscription content, log in to check access.

References

  1. Agmon S (1965) Elliptic boundary value problems. Van Nostrand, New YorkGoogle Scholar
  2. Jones DS, Plank MJ, Sleeman BD (2010) Differential equations and mathematical biology, 2nd edn. Chapman and Hall/CRC, Boca RatonGoogle Scholar
  3. Murray JD (1993) Mathematical biology. Springer, BerlinGoogle Scholar
  4. Ockendon J, Howison S, Lacey A, Movchan A (1999) Applied partial differential equations. Oxford University Press, OxfordGoogle Scholar
  5. Protter MH, Weinberger HF (1984) Maximum principles in differential equations. Springer, BerlinGoogle Scholar
  6. Roose T, Chapman SJ, Maini PK (2007) Mathematical models of avascular tumor growth. SIAM Rev 49(2):179–208Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2013

Authors and Affiliations

  1. 1.School of MathematicsUniversity of LeedsLeedsUK