Abstract
For a finite system of impulse parabolic equations some comparison theorems and flow invariance results are obtained using the method of upper and lower solutions. These results can be used for the mathematical modelling of population dynamics systems with abrupt changes implied by diseases, harvesting or heavy immigration.
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References
D. Bainov -Z. Kamont -E. Minchev,First order impulsive partial differential inequalities, Appl. Math. Comput.,61 (1994), pp. 207–230.
D. D. Bainov -P. S. Simeonov,Systems with Impulse Effect, Stability Theory and Applications, Ellis Horwood, Chichester (1989).
C. Y. Chan -L. Ke -A. S. Vatsala,Impulsive quenching for reaction-diffusion equations, Nonlinear Analysis,22 (1994), pp. 1323–1328.
L. H. Erbe -H. I. Freedman -X. Z. Liu -J. H. Wu,Comparison principles for impulsive parabolic equations with applications to models of single species growth, J. Austral. Math. Soc. Ser. B,32 (1991), pp. 382–400.
D. Henry,Geomeltric Theory of Semilinear Parabolic Equations, Springer-Verlag, Berlin-New York (1981).
M.Kirane - Yu. V.Rogovchenko,Comparison results for systems of impulse parabolic equaltions with applications to population dynamics, to appear in Nonlinear Analysis.
G. S. Ladde -V. Lakshmikantham -A. S. Vatsala,Monotone Iterative Techniques for Nonlinear Differential Equations, Pitman, Boston (1985).
V. Lakshmikantham -D. D. Bainov -P. S. Simeonov,Theory of Impulsive Differential Equations, World Scientific, Singapore (1989).
S. P. Rogovchenko,Periodic solutions of hyperbolic systems with fixed times of impulse action, Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint, 8 (1988), pp. 1–39 (in Russian).
S. P. Rogovchenko -Yu. V. Rogovchenko,Periodic solutions of a weakly nonlinear hyperbolic impulse system, inAsymptotic Integration of Nonlinear Equations (ed.Yu. A. Mitropolskii), Akad. Nauk Ukrainy, Inst. Mat., Kiev (1992), pp. 97–103 (in Russian).
Yu. V. Rogovchenko -S. I. Trofimchuk,Periodic solutions of weakly nonlinear partial differential equations of parabolic type with impulse action and their stability, Akad. Nauk Ukrain. SSR, Inst. Mat. Preprint,65 (1986), pp. 1–44 (in Russian).
Yu. V. Rogovchenko -S. I. Trofimchuk,Bounded and periodic solutions of weakly nonlinear impulse evolutionary systems, Ukrain. Mat. Zh.,39 (1987), pp. 260–264 (in Russian).
Yu. V.Rogovchenko - S. I.Trofimchuk,Existence and stability properties of solutions of impulse evolution systems with applications to population dynamics, to appear.
A. M. Samoilenko -M. Ilolov,Nonhomogeneous evolution equations with impulse action, Ukrainian Math. J.,44 (1992), pp. 83–90.
A. M. Samoilenko -M. Ilolov,On the theory of time-inhomogeneous evolution equations with impulse action, Soviet Math. Dokl.,44 (1992), pp. 59–63.
A. M. Samoilenko -N. Perestyuk,Differential Equations with Impulse Action, Vishcha Shkola, Kiev (1987) (in Russian).
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Rogovchenko, Y.V. Comparison principles for systems of impulsive parabolic equations. Annali di Matematica pura ed applicata 170, 311–328 (1996). https://doi.org/10.1007/BF01758993
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DOI: https://doi.org/10.1007/BF01758993