Advanced search
Publication Cover
Applicable Analysis
An International Journal
Volume 97, 2018 - Issue 16
Submit an article Journal homepage
187
Views
0
CrossRef citations to date
0
Altmetric
Articles

A free boundary problem for a class of nonlinear nonautonomous size-structured population model

Wenbin LvSchool of Mathematical Sciences, Shanxi University, Taiyuan, China.Correspondence[email protected]
ORCID Iconhttp://orcid.org/0000-0001-5760-5578
ORCID Icon &
Shaohua WuSchool of Mathematics and Statistics, Wuhan University, Wuhan, China.
Pages 2852-2864 | Received 01 Oct 2016, Accepted 19 Oct 2017, Published online: 01 Nov 2017

References

  • Chen GQ, Shahgholian H, Vazquez JL. Free boundary problems: the forefront of current and future developments. Philos Trans Ser A Math Phys Eng Sci. 2015;373(2050):814–820.
  • Friedman A. Free boundary problems in science and technology. Not AMS. 2000;47(8):854–861.
  • Taylor ME. Partial differential equations III. Vol. 116. New York (NY): Springer Science and Business Media; 2013.
  • Guan CH, Yi FH. A free boundary problem arising from a stochastic optimal control model under controllable risk. J Differ Equ. 2016;260(6):4845–4870.
  • Qin C, Chen XF, Lai X, et al. Regularity of free boundary arising from optimal exercise of perpetual executive stock options. Interfaces Free Boundaries. 2015;17(1):69–92.
  • Chen H, Wu SH. The moving boundary problem in a chemotaxis model. Commun Pure Appl Anal. 2012;11(2):735–746.
  • Cui SB. Linearized stability for a multi-dimensional free boundary problem modelling two-phase tumour growth. Nonlinearity. 2014;27(5):1045–1079.
  • Du YH, Lin ZG. The diffusive competition model with a free boundary: invasion of a superior or inferior competitor. Discrete Continuous Dyn Syst Ser B. 2014;19(10):3105–3132.
  • Banks HT, Kappel F, Wang C. A semigroup formulation of a nonlinear size-structured distributed rate population model. In: Control and estimation of distributed parameter systems: nonlinear phenomena. Basel: Springer; 1994. p. 1–19.
  • Sinko JW, Streifer W. A new model for age-size structure of a population. Ecology. 1967;48(6):910–918.
  • Ackleh AS. Parameter estimation in a structured algal coagulation-fragmentation model. Nonlinear Anal Theory Methods Appl. 1997;28(5):837–854.
  • Calsina A, Saldaña J. A model of physiologically structured population dynamics with a nonlinear individual growth rate. J Math Biol. 1995;33(4):335–364.
  • Ackleh AS, Deng K. Existence-uniqueness of solutions for a nonlinear nonautonomous size-structured population model: an upper-lower solution approach. Can Appl Math Q. 2000;8(1):1–15.
  • Brezis H. Functional analysis. Sobolev spaces and partial differential equations. New York (NY): Springer Science and Business Media; 2010.
  • Ackleh AS, Deng K. Monotone method for first order nonlocal hyperbolic initial-boundary value problems. Applicable Anal. 1997;67(3–4):283–293.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.