Discrete and Continuous Dynamical Systems - Series B (DCDS-B)

Advection control in parabolic PDE systems for competitive populations
Pages: 1049 - 1072, Issue 3, May 2017

doi:10.3934/dcdsb.2017052      Abstract        References        Full text (1311.0K)           Related Articles

Kokum R. De Silva - Department of Mathematics, University of Peradeniya, Peradeniya, KY 20400, Sri Lanka (email)
Tuoc V. Phan - Department of Mathematics, University of Tennessee, Knoxville, TN 37996-1320, United States (email)
Suzanne Lenhart - University of Tennessee, Department of Mathematics, 227 Ayres Hall, 1403 Circle Drive, Knoxville, TN 37996-1320, United States (email)

1 F. Belgacem and C. Cosner, The effects of dispersal along environmental gradients on the dynamics of populations in heterogeneous environment, Canadian Applied Mathematics Quarterly, 3 (1995), 379-397.       
2 R. S. Cantrell and C. Cosner, Diffusive logistic equations with indefinite weights: Population models in disrupted environments II, SIAM J. Math. Anal., 22 (1991), 1043-1064.       
3 R. S. Cantrell and C. Cosner, The effects of spatial heterogeneity in population dynamics, Journal of Mathematical Biology, 29 (1991), 315-338.       
4 R. S. Cantrell and C. Cosner, Spatial Ecology via Reaction-Diffusion Equations, Wiley Series in Mathematical and Computational Biology, 2003.       
5 R. S. Cantrell, C. Cosner and Y. Lou, Advection-mediated coexistence of competing species, Proceedings of the Royal Society of Edinburgh Section A, 137 (2007), 497-518.       
6 C. Cosner and Y. Lou, Does movement towards better environments always benefit a population?, Journal of Mathematical analysis and Applications, 277 (2003), 489-503.       
7 W. Ding, H. Finotti, S. Lenhart, Y. Lou and Q. Ye, Optimal control of growth coefficient on a steady-state population model, Nonlinear Analysis: Real World Applications, 11 (2010), 688-704.       
8 L. C. Evans, Partial Differential Equations, $2^{nd}$ edition, American Mathematical Society, Providence, RI, 2010.       
9 H. Finotti, S. Lenhart and T. V. Phan, Optimal control of advective direction in reaction-diffusion population models, Evolution equations and control theory, 1 (2012), 81-107.       
10 W. Hackbusch, A numerical method for solving parabolic equations with opposite orientations, Computing, 20 (1978), 229-240.       
11 M. R. Kelly, Jr. Y. Xing and S. Lenhart, Optimal fish harvesting for a population modeled by a nonlinear parabolic partial differential equation, Natural Resources Modeling Journal, 29 (2016), 36-70.       
12 S. Lenhart and J. T. Workman, Optimal Control Applied to Biological Models, Chapman and Hall/CRC Mathematical and Computational Biology Series, 2007.       
13 J. Simon, Compact sets in the $L^p(0,T;B)$, Annali di Matematica Pure ed Applicata, 146 (1987), 65-96.       

Go to top