Analysis and discretization of an optimal control problem for the forced fisher equation

Discrete and Continuous Dynamical Systems - Series B

Volumn 8, Issue 3, 2007, Pages 569-587

  Gunzburger, Max ^a   Yang, Sung Dae ^a   Zhu, Wenxiang ^b  

^a FLORIDA STATE UNIVERSITY   (United States)

^b Nucl Eng Idaho State University   (United States)

Author keywords

Existence of optimal controls; Finite element methods; Forced fisher equation; Optimality systems

Indexed keywords

EID: 35348983510     PISSN: 15313492     EISSN: None     Source Type: Journal    
DOI: 10.3934/dcdsb.2007.8.569     Document Type: Conference Paper

References (18)

1. R. Adams, "Sobolev Spaces," Academic, New York, 1975.
2. D. Aronson, H. Weinberger, Partial differential equations and related topics, in Lecture Notes in Math., 446, Springer, New York, (1975).
3. D. Aronson, H. Weinberger, Multidimensional nonlinear diffusions arising in population genetics, Adv. Math., 30 Springer, New York, (1978), 33-76.
4. F. Brezzi, J. Rappaz, and P. Raviart, Finite dimensional approximation of nonlinear problems. Part I: Branches of nonsingular solutions, Numer. Math, 36 (1980), 1-25.
5. N. F. Britton, "Reaction-Diffusion Equations and Their Applications to Biology," Academic Press, New York, 1986.
6. K. Chrysafinos, L. S. Hou, Error estimates for semidiscrete finite element approximations of linear and semilinear parabolic equations under minimal regularity asssumptions, SIAM J. Numer. Anal., 40 (2002), 282-306.
7. T. Cazenave and A. Haraux, "An Introduction to Semilinear Evolution Equations," Clarendon Press, Oxford, 1998.
8. P. Ciarlet, "The Finite Element Method for Elliptic Problems," North-Holland, Amsterdam, 1978.
9. P. Fife, "Mathematical Aspects of Reacting and Diffusing Systems," Lecture Notes in Biomath., 28, Springer, Berlin, 1979.
10. R. Fisher, The advanced of advantageous genes, Ann. Eugenics, 7 (1937), 335-369.
11. W. Fleming, A selection-migration model in population genetics, J. Math. Biol., 2 (1975), 219-233.
12. A. Fursikov, "Optimal Control of Distributed Systems. Theory and Applications," American Mathematical Society, Providence, Rhode Island, 2000.
13. J.-L. Lions, "Control of Distributed Singular Systems," Bordas, Paris, 1983.
14. M. Gunzburger, L. Hou, and W. Zhu, Modeling and analysis of the forced Fisher equation, Nonl. Anal., 62 (2005), 19-40.
15. J. D. Murray, "Mathematical Biology," Springer, Berlin, 1989.
16. R. Temam, "Navier-Stokes Equations," North-Holland, Amsterdam, 1985.
17. R. Temam, "Infinite-Dimensional Dynamical Systems in Mechanics and Physics," Springer-Verlag, Providence, New York, 1988.
18. V. Thomme, "Galerkin Finite Element Methods for Parabolic Equations," Springer, Berlin, 1997.