Institute of Mathematics

References:
[1] B. Ainseba: Exact and approximate controllability of the age and space population dynamics structured model. J. Math. Anal. Appl. 275 (2002), 562-574. DOI 10.1016/S0022-247X(02)00238-X | MR 1943766 | Zbl 1005.92023
[2] B. Ainseba: Corrigendum to "Exact and approximate controllability of the age and space population dynamics structured model" (J. Math. Anal. Appl. 275 (2) (2002), 562-574). J. Math. Anal. Appl. 393 (2012), 328. DOI 10.1016/j.jmaa.2012.01.059 | MR 2921673 | Zbl 1260.92095
[3] B. Ainseba, S. Aniţa: Local exact controllability of the age-dependent population dynamics with diffusion. Abstr. Appl. Anal. 6 (2001), 357-368. DOI 10.1155/S108533750100063X | MR 1880930 | Zbl 0995.93008
[4] B. Ainseba, S. Aniţa: Internal exact controllability of the linear population dynamics with diffusion. Electron. J. Differ. Equ. 2004 (2004), Article ID 112, 11 pages. MR 2108883 | Zbl 1134.93311
[5] B. Ainseba, S. Aniţa: Internal stabilizability for a reaction-diffusion problem modeling a predator-prey system. Nonlinear Anal., Theory Methods Appl., Ser. A 61 (2005), 491-501. DOI 10.1016/j.na.2004.09.055 | MR 2126609 | Zbl 1072.35090
[6] B. Ainseba, Y. Echarroudi, L. Maniar: Null controllability of a population dynamics with degenerate diffusion. Differ. Integral Equ. 26 (2013), 1397-1410. MR 3129015 | Zbl 1313.35193
[7] B. Ainseba, M. Langlais: On a population dynamics control problem with age dependence and spatial structure. J. Math. Anal. Appl. 248 (2000), 455-474. DOI 10.1006/jmaa.2000.6921 | MR 1776023 | Zbl 0964.93045
[8] E. M. Ait Ben Hassi, F. Ammar Khodja, A. Hajjaj, L. Maniar: Null controllability of degenerate parabolic cascade systems. Port. Math. (N.S.) 68 (2011), 345-367. DOI 10.4171/PM/1895 | MR 2832802 | Zbl 1231.35103
[9] F. Alabau-Boussouira, P. Cannarsa, G. Fragnelli: Carleman estimates for degenerate parabolic operators with applications to null controllability. J. Evol. Equ. 6 (2006), 161-204. DOI 10.1007/s00028-006-0222-6 | MR 2227693 | Zbl 1103.35052
[10] S. Aniţa: Analysis and Control of Age-Dependent Population Dynamics. Mathematical Modelling: Theory and Applications 11. Kluwer Acadamic, Dordrecht (2000). DOI 10.1007/978-94-015-9436-3 | MR 1797596 | Zbl 0960.92026
[11] N. Apreutesei, G. Dimitriu: On a prey-predator reaction-diffusion system with Holling type III functional response. J. Comput. Appl. Math. 235 (2010), 366-379. DOI 10.1016/j.cam.2010.05.040 | MR 2677695 | Zbl 1205.65274
[12] V. Barbu, M. Iannelli, M. Martcheva: On the controllability of the Lotka-McKendrick model of population dynamics. J. Math. Anal. Appl. 253 (2001), 142-165. DOI 10.1006/jmaa.2000.7075 | MR 1804594 | Zbl 0961.92024
[13] I. Boutaayamou, Y. Echarroudi: Null controllability of population dynamics with interior degeneracy. Electron. J. Differ. Equ. 2017 (2017), Article ID 131, 21 pages. MR 3665593 | Zbl 1370.35183
[14] I. Boutaayamou, G. Fragnelli: A degenerate population system: Carleman estimates and controllability. Nonlinear Anal., Theory Methods Appl., Ser. A 195 (2020), Article ID 111742, 29 pages. DOI 10.1016/j.na.2019.111742 | MR 4052601 | Zbl 1435.35398
[15] I. Boutaayamou, J. Salhi: Null controllability for linear parabolic cascade systems with interior degeneracy. Electron. J. Differ. Equ. 2016 (2016), Article ID 305, 22 pages. MR 3604750 | Zbl 1353.35184
[16] T. Cabello, M. Gámez, Z. Varga: An improvement of the Holling type III functional response in entomophagous species model. J. Biol. Syst. 15 (2007), 515-524. DOI 10.1142/S0218339007002325 | Zbl 1146.92326
[17] M. Campiti, G. Metafune, D. Pallara: Degenerate self-adjoint evolution equations on the unit interval. Semigroup Forum 57 (1998), 1-36. DOI 10.1007/PL00005959 | MR 1621852 | Zbl 0915.47029
[18] P. Cannarsa, G. Fragnelli: Null controllability of semilinear degenerate parabolic equations in bounded domains. Electron. J. Differ. Equ. 2006 (2006), Article ID 136, 20 pages. MR 2276561 | Zbl 1112.35335
[19] P. Cannarsa, G. Fragnelli, D. Rocchetti: Null controllability of degenerate parabolic with drift. Netw. Heterog. Media 2 (2007), 695-715. DOI 10.3934/nhm.2007.2.695 | MR 2357764 | Zbl 1140.93011
[20] P. Cannarsa, G. Fragnelli, D. Rocchetti: Controllability results for a class of one-dimensional degenerate parabolic problems in nondivergence form. J. Evol. Equ. 8 (2008), 583-616. DOI 10.1007/s00028-008-0353-34 | MR 2460930 | Zbl 1176.35108
[21] P. Cannarsa, G. Fragnelli, J. Vancostenoble: Linear degenerate parabolic equations in bounded domains: Controllability and observability. Systems, Control, Modeling and Optimization. IFIP International Federation for Information Processing 202. Springer, New York (2006), 163-173. DOI 10.1007/0-387-33882-9_15 | MR 2241704 | Zbl 1214.93021
[22] P. Cannarsa, G. Fragnelli, J. Vancostenoble: Regional controllability of semilinear degenerate parabolic equations in bounded domains. J. Math. Anal. Appl. 320 (2006), 804-818. DOI 10.1016/j.jmaa.2005.07.006 | MR 2225996 | Zbl 1177.93016
[23] P. Cannarsa, P. Martinez, J. Vancostenoble: Persistent regional null controllability for a class of degenerate parabolic equations. Commun. Pure Appl. Anal. 3 (2004), 607-635. DOI 10.3934/cpaa.2004.3.607 | MR 2106292 | Zbl 1063.35092
[24] P. Cannarsa, P. Martinez, J. Vancostenoble: Null controllability of degenerate heat equations. Adv. Differ. Equ. 10 (2005), 153-190. MR 2106129 | Zbl 1145.35408
[25] J. H. P. Dawes, M. O. Souza: A derivation of Holling's type I, II and III functional responses in predator-prey systems. J. Theor. Biol. 327 (2013), 11-22. DOI 10.1016/j.jtbi.2013.02.017 | MR 3046076 | Zbl 1322.92056
[26] Y. Echarroudi, L. Maniar: Null controllability of a model in population dynamics. Electron. J. Differ. Equ. 2014 (2014), Article ID 240, 20 pages. MR 3291740 | Zbl 06430755
[27] Y. Echarroudi, L. Maniar: Null controllability of a degenerate cascade model in population dynamics. Studies in Evolution Equations and Related Topics STEAM-H: Science, Technology, Engineering, Agriculture, Mathematics & Health. Springer, Cham (2021), 211-268. DOI 10.1007/978-3-030-77704-3_10 | Zbl 07464638
[28] G. Fragnelli: An age-dependent population equation with diffusion and delayed birth process. Int. J. Math. Math. Sci. 2005 (2005), 3273-3289. DOI 10.1155/IJMMS.2005.3273 | MR 2208054 | Zbl 1084.92029
[29] G. Fragnelli: Null controllability of degenerate parabolic equations in non divergence form via Carleman estimates. Discrete Contin. Dyn. Syst., Ser. S 6 (2013), 687-701. DOI 10.3934/dcdss.2013.6.687 | MR 3010677 | Zbl 1258.93025
[30] G. Fragnelli: Carleman estimates and null controllability for a degenerate population model. J. Math. Pures Appl. (9) 115 (2018), 74-126. DOI 10.1016/j.matpur.2018.01.003 | MR 3808342 | Zbl 1391.35238
[31] G. Fragnelli: Null controllability for a degenerate population model in divergence form via Carleman estimates. Adv. Nonlinear Anal. 9 (2020), 1102-1129. DOI 10.1515/anona-2020-0034 | MR 4019739 | Zbl 1427.35141
[32] G. Fragnelli, A. Idrissi, L. Maniar: The asymptotic behavior of a population equation with diffusion and delayed birth process. Discrete Contin. Dyn. Syst., Ser. B 7 (2007), 735-754. DOI 10.3934/dcdsb.2007.7.735 | MR 2291870 | Zbl 1211.35046
[33] G. Fragnelli, P. Martinez, J. Vancostenoble: Qualitative properties of a population dynamics system describing pregnancy. Math. Models Methods Appl. Sci. 15 (2005), 507-554. DOI 10.1142/S0218202505000455 | MR 2137524 | Zbl 1092.92037
[34] G. Fragnelli, D. Mugnai: Carleman estimates and observability inequalities for parabolic equations with interior degeneracy. Adv. Nonlinear Anal. 2 (2013), 339-378. DOI 10.1515/anona-2013-0015 | MR 3199737 | Zbl 1282.35101
[35] G. Fragnelli, D. Mugnai: Carleman estimates, observability inequalities and null controllability for interior degenerate non smooth parabolic equations. Mem. Am. Math. Soc. 1146 (2016), 88 pages. DOI 10.1090/memo/1146 | MR 3498150 | Zbl 1377.93043
[36] G. Fragnelli, L. Tonetto: A population equation with diffusion. J. Math. Anal. Appl. 289 (2004), 90-99. DOI 10.1016/j.jmaa.2003.08.047 | MR 2020529 | Zbl 1109.34042
[37] A. V. Fursikov, O. Y. Imanuvilov: Controllability of Evolutions Equations. Lecture Notes Series, Seoul 34. Seoul National University, Seoul (1996). MR 1406566 | Zbl 0862.49004
[38] A. Hajjaj, L. Maniar, J. Salhi: Carleman estimates and null controllability of degenerate/singular parabolic systems. Electron. J. Differ. Equ. 2016 (2016), Article ID 292, 25 pages. MR 3578313 | Zbl 1353.35186
[39] N. Hegoburu, M. Tucsnak: Null controllability of the Lotka-Mckendrick system with spatial diffusion. Math. Control Relat. Fields 8 (2018), 707-720. DOI 10.3934/mcrf.2018030 | MR 3917460 | Zbl 1417.92131
[40] Y. Jia, J. Wu, H.-K. Xu: Positive solutions of a Lotka-Volterra competition model with cross-diffusion. Comput. Math. Appl. 68 (2014), 1220-1228. DOI 10.1016/j.camwa.2014.08.016 | MR 3272537 | Zbl 1367.92129
[41] A. Juska, L. Gouveia, J. Gabriel, S. Koneck: Negotiating bacteriological meat contamination standards in the US: The case of $ E. Coli$ O157:H7. Sociologia Ruralis 40 (2000), 249-271. DOI 10.1111/1467-9523.00146
[42] R. E. Kooij, A. Zegeling: A predator-prey model with Ivlev's functional response. J. Math. Anal. Appl. 198 (1996), 473-489. DOI 10.1006/jmaa.1996.0093 | MR 1376275 | Zbl 0851.34030
[43] M. Langlais: A nonlinear problem in age-dependent population diffusion. SIAM J. Math. Anal. 16 (1985), 510-529. DOI 10.1137/0516037 | MR 0783977 | Zbl 0589.92013
[44] B. Liu, Y. Zhang, L. Chen: Dynamics complexities of a Holling I predator-prey model concerning periodic biological and chemical control. Chaos Solitons Fractals 22 (2004), 123-134. DOI 10.1016/j.chaos.2003.12.060 | MR 2057553 | Zbl 1058.92047
[45] X. Liu, Q. Huang: The dynamics of a harvested predator-prey system with Holling type IV functional response. Biosystems 169-170 (2018), 26-39. DOI 10.1016/j.biosystems.2018.05.005
[46] A. Y. Mozorov: Emergence of Holling type III zooplankton functional response: Bringing together field evidence and mathematical modelling. J. Theor. Biol. 265 (2010), 45-54. DOI 10.1016/j.jtbi.2010.04.016 | MR 2981553 | Zbl 1406.92676
[47] L. Pavel: Classical solutions in Sobolev spaces for a class of hyperbolic Lotka-Volterra systems. SIAM J. Control Optim. 51 (2013), 2132-2151. DOI 10.1137/090767303 | MR 3053572 | Zbl 1275.35138
[48] R. Peng, J. Shi: Non-existence of non-constant positive steady states of two Holling type-II predator-prey systems: Strong interaction case. J. Differ. Equations 247 (2009), 866-886. DOI 10.1016/j.jde.2009.03.008 | MR 2528495 | Zbl 1169.35328
[49] S. Piazzera: An age-dependent population equation with delayed birth process. Math. Methods Appl. Sci. 27 (2004), 427-439. DOI 10.1002/mma.462 | MR 2034234 | Zbl 1038.35145
[50] M. A. Pozio, A. Tesei: Degenerate parabolic problems in population dynamics. Japan J. Appl. Math. 2 (1985), 351-380. DOI 10.1007/BF03167082 | MR 0839335
[51] A. Pugliese, L. Tonetto: Well-posedness of an infinite system of partial differential equations modelling parasitic infection in age-structured host. J. Math. Anal. Appl. 284 (2003), 144-164. DOI 10.1016/S0022-247X(03)00295-6 | MR 1996124 | Zbl 1039.35130
[52] A. Rhandi, R. Schnaubelt: Asymptotic behaviour of a non-autonomous population equation with diffusion in $L^1$. Discrete Contin. Dyn. Syst. 5 (1999), 663-683. DOI 10.3934/dcds.1999.5.663 | MR 1696337 | Zbl 1002.92016
[53] J. Salhi: Null controllability for a coupled system of degenerate/singular parabolic equations in nondivergence form. Electron. J. Qual. Theory Differ. Equ. 2018 (2018), Article ID 31, 28 pages. DOI 10.14232/ejqtde.2018.1.31 | MR 3811494 | Zbl 1413.35269
[54] G. Seo, D. L. DeAngelis: A predator-prey model with a Holling type I functional response including a predator mutual interference. J. Nonlinear Sci. 21 (2011), 811-833. DOI 10.1007/s00332-011-9101-6 | MR 2860930 | Zbl 1238.92049
[55] G. T. Skalski, J. F. Gilliam: Functional responses with predator interference: Viable alternatives to the Holling type II model. Ecology 82 (2001), 3083-3092. DOI 10.1890/0012-9658(2001)082[3083:FRWPIV]2.0.CO;2
[56] O. Traore: Null controllability of a nonlinear population dynamics problem. Int. J. Math. Math. Sci. 2006 (2006), Article ID 49279, 20 pages. DOI 10.1155/IJMMS/2006/49279 | MR 2268531 | Zbl 1127.93017
[57] W. Wang, L. Zhang, H. Wang, Z. Li: Pattern formation of a predator-prey system with Ivlev-type functional response. Ecological Modelling 221 (2010), 131-140. DOI 10.1016/j.ecolmodel.2009.09.011
[58] G. F. Webb: Population models structured by age, size, and spatial position. Structured Population Models in Biology and Epidemiology. Lecture Notes in Mathematics 1936. Springer, Berlin (2008), 1-49. DOI 10.1007/978-3-540-78273-5_1 | MR 2433574
[59] Y. Zhang, Z. Xu, B. Liu, L. Chen: Dynamic analysis of a Holling I predator-prey system with mutual interference concerning pest control. J. Biol. Syst. 13 (2005), 45-58. DOI 10.1142/S0218339005001392 | Zbl 1073.92061
[60] C. Zhao, M. Wang, P. Zhao: Optimal control of harvesting for age-dependent predator-prey system. Math. Comput. Modelling 42 (2005), 573-584. DOI 10.1016/j.mcm.2004.07.019 | MR 2173475 | Zbl 1088.92063