Skip to main content

Existence and Uniqueness of Strong Solution for Predator-Prey System of Three Species with Age-Structure

  • Conference paper
  • 1782 Accesses

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 224))

Abstract

In this paper, existence and uniqueness of strong solution are proved for predator-prey system of three species with age-structure in Hilbert space. Using Gronwall’s lemma, some criteria of existence and uniqueness of strong solution are obtained for predator-prey system of three species with age-structure.

This work is partially supported by NingXia Natural Science Foundation # NZ0935 and CNSF Grant # 11061024.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Rorres, C., Fair, W.: Optimal age specific harvesting policy for continuous-time population model. In: Burton, T.A. (ed.) Modelling and Differential Equations in Biology. Dekker, New York (1980)

    Google Scholar 

  2. Chan, W.L., Guo, B.Z.: Optimal birth control of population dynamics. J. Math. Anal. Appl. 144, 532–552 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Chan, W.L., Guo, B.Z.: Optimal birth control of population dynamics. Part 2. Problems with free final time, phase constraints, and mini-max costs. J. Math. Anal. Appl. 146, 523–539 (1990)

    Article  MathSciNet  MATH  Google Scholar 

  4. Anita, S.: Optimal harvesting for a nonlinear age-dependent population dynamics. J. Math. Anal. Appl. 226, 6–22 (1998)

    Article  MathSciNet  MATH  Google Scholar 

  5. Ainseba, B., Langlais, M.: On a population dynamics control problem With age dependent and patial structure. J. Math. Anal. App. 248, 455–474 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  6. Albrecht, F., Gatzke, H., Haddad, A., Wax, N.: On the control of certain interacting population. J. Math. Anal. Appl. 53, 578–603 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  7. Lenhart, S., Liang, M., Protopopescu, V.: Optimal control of boundary habitat hostility for interacting species. Math. Mech. Appl. Sci. 22, 1061–1077 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  8. Crespo, L.G., Sun, J.Q.: Optimal control of population of competing species. Nonlinear Dynam. 27, 197–210 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  9. Luo, Z., He, Z.-R., Li, W.-T.: Optimal birth control for predator system of three species with age-structure. Applied Mathematics and Computation 155, 665–685 (2004)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Li-Yu, C., Qi-Min, Z. (2011). Existence and Uniqueness of Strong Solution for Predator-Prey System of Three Species with Age-Structure. In: Zeng, D. (eds) Applied Informatics and Communication. ICAIC 2011. Communications in Computer and Information Science, vol 224. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-23214-5_77

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-23214-5_77

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-23213-8

  • Online ISBN: 978-3-642-23214-5

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics