Optimal control of harvesting coupled with boundary control in a predator—prey system

References

• Bierregaard , R. , Lovejoy , T. , Kapos , V. , Augusto dos Santos , A. and Hutchings , R. 1992 . The biological dynamics of tropical rainforest fragments . BioScience , 24 ( 11 ) : 859 – 866 .
   Google Scholar
• Cañada , A. , Gámez , J.L. and Montero , J.A. 1994 . An optimal control problem for a nonlinear elliptic equation arising from, population dynamics , Spain : University of Granada . preprint
   Google Scholar
• Cantrell , R.S. , Cosner , C. and Fagan , W.F. 1988 . Competitive reversals inside ecological reserves: the role of external habitat degradation , preprint .
   Google Scholar
• Cosner C. private communication 1999
   Google Scholar
• Evans , L.C. 1988 . “ Partial Differential Equations ” . In American Mathematical Society , Providence .
   Google Scholar
• Evans , L.C. 1990 . “ Weak convergence methods for nonlinear partial differential equations ” . In American Mathematical Society , Vol. 74 , Providence .
   Google Scholar
• Fister , K.R. 1997 . Optimal control of harvesting in a predator—prey parabolic system . Houston Journal of Mathematics , 23 ( 2 ) : 341 – 355 .
   Web of Science ®Google Scholar
• Fister , K. R. and Lenhart , S. 1998 . Positive profit in a predator—prey situation in Mathematical Models in Medical and Health Science , Edited by: Ann Horn , Mary , Simonett , Gieri and Webb , Glenn F. 129 – 137 . Nashville : Vanderbilt University Press .
   Google Scholar
• Friesen , L. , Eagles , P.F.J. and Mackay , R.J. 1995 . Effects of residential development on forest—dwelling neotropical migrant songbirds . Conservation Biology , 9 ( 6 ) : 1408 – 1414 .
   Web of Science ®Google Scholar
• Goh , B.S. , Leitmann , G. and Vincent , T.L. 1974 . “ Optimal control of a prey—predator system ” . In Mathematical Biosciences , Vol. 19 , American Elsevier Publishing Company, Inc .
   Google Scholar
• Ladyzenskaja , O.A. , Solonnikov , V.A. and Ural'ceva , N.N. 1968 . “ Linear and QuasiLinear Equations of Parabolic Type ” . In American Mathematical Society , Vol. 23 , Providence .
   Google Scholar
• Lenhart , S. , Liang , M. and Protopopescu , V. 1999 . Optimal control of boundary habitat hostility for interacting species , preprint .
   Google Scholar
• Leung , A.W. 1993 . “ Optimal control for nonlinear systems of partial differential equation related to ecology ” . In Institute of Mathematical Sciences and Applications preprint series , Vol. 1126 , University of Cincinnati .
   Google Scholar
• Leung , A.W. 1995 . Optimal harvesting coefficient control of steady—state prey—predator diffusive Volterra—Lotka systems . Applied Mathematics and Optimization , 32 : 219 – 241 .
   Google Scholar
• Leung , A.W. 1989 . Systems of Nonlinear Partial Differential Equations, Applications to Biology and Engineering , Dordrecht, Boston : Kluwer Academics Publishers .
   Google Scholar
• Li , X. and Yong , J. 1995 . Optimal Control Theory for Infinite Dimensional Systems , Boston : Birkhauser .
   Google Scholar
• Lions , J.L. 1971 . Optimal Control of Systems Governed by Partial Differential Equations , New York : Springer—Verlag .
   Google Scholar
• Mesterton—gibbons , M. 1996 . A technique for finding optimal two—species harvesting policies . Ecological Modelling , 92 : 235 – 244 .
   Web of Science ®Google Scholar
• Okubo , A. 1980 . Diffusion and Ecological Problems: Mathematical Models , Berlin : Springer—Verlag .
   Google Scholar
• Protter , M.H. and Weinberger , H.F. 1967 . Maximum Principles in Differential Equations , Englewood Cliffs : Prentice—Hall Inc .
   Google Scholar
• Redlinger , R. 1998 . Pointwise a priori bounds for strongly coupled semilinear parabolic systems . Indiana University Mathematics Journal , 36 ( 2 ) : 441 – 454 .
   Google Scholar
• Simon , J. 1987 . Compact sets in the space Lp(0, T; B) . Annali di Matematica Pura and Applicata , CXLVI ( 2 ) : 65 – 96 .
   Google Scholar