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A nonlocal Dirichlet problem with impulsive action: estimates of the growth for the solutions
Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1119-1128.

Through this paper we deal with the asymptotic behaviour as t+ of the solutions for a nonlocal diffusion problem with impulsive actions and Dirichlet condition. We establish a decay rate for the solutions assuming appropriate hypotheses on the impulsive functions and the nonlinear reaction.

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DOI : 10.5802/crmath.109
Jaqueline da Costa Ferreira 1 ; Marcone Corrêa Pereira 2

1 Depto. Matemática, CCE, Universidade Federal do Espírito Santo, Av. Fernando Ferrari 514, Vitória - ES, Brazil
2 Depto. Matemática Aplicada, IME, Universidade de São Paulo, Rua do Matão 1010, São Paulo - SP, Brazil
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits
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     title = {A nonlocal {Dirichlet} problem with impulsive action: estimates of the growth for the solutions},
     journal = {Comptes Rendus. Math\'ematique},
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Jaqueline da Costa Ferreira; Marcone Corrêa Pereira. A nonlocal Dirichlet problem with impulsive action: estimates of the growth for the solutions. Comptes Rendus. Mathématique, Volume 358 (2020) no. 11-12, pp. 1119-1128. doi : 10.5802/crmath.109. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.109/

[1] Dimitrov D. Bainov; Emil Minchev; Kiyokazu Nakagawa Asymptotic behaviour of solutions of impulsive semilinear parabolic equation, Nonlinear Anal., Theory Methods Appl., Volume 30 (1997) no. 5, pp. 2725-2734 | DOI | MR | Zbl

[2] Peter W. Bates; Paul C. Fife; Xiaofeng Ren; Xuefeng Wang Travelling waves in a convolution model for phase transitions, Arch. Ration. Mech. Anal., Volume 138 (1997) no. 2, pp. 105-136 | DOI | Zbl

[3] Rafael D. Benguria; Marcone C. Pereira Remarks on the spectrum of a nonlocal Dirichlet problem (2019) (https://arxiv.org/abs/1911.05803v3)

[4] Abdelkader Boucherif; Ali S. Al-Qahtani; Bilal Chanane Existence of solutions for impulsive parabolic partial differential equations, Numer. Funct. Anal. Optim., Volume 36 (2015) no. 6, pp. 730-747 | DOI | MR | Zbl

[5] Xinfu Chen Existence, uniqueness and asymptotic stability of travelling waves in nonlocal evolution equations, Adv. Differ. Equ., Volume 2 (1997) no. 1, pp. 125-160 | Zbl

[6] Carmen Cortazar; Manuel Elgueta; Julio D. Rossi Nonlocal diffusion problems that approximate the heat equation with Dirichlet boundary conditions, Isr. J. Math., Volume 170 (2009), pp. 53-60 | DOI | MR | Zbl

[7] Paul C. Fife Some nonclassical trends in parabolic and parabolic-like evolutions, Trends in Nonlinear Analysis. On the occasion of the 60th birthday of Willi Jäger, Springer, 2003, pp. 153-191 | DOI | Zbl

[8] Jorge García-Melián; Julio D. Rossi On the principal eigenvalue of some nonlocal diffusion problems, J. Differ. Equations, Volume 246 (2009) no. 1, pp. 21-38 | DOI | MR | Zbl

[9] Eduardo M. Hernández; Sueli M. Tanaka Aki; Hernán Henríquez Global solutions for impulsive abstract partial differential equations, Comput. Math. Appl., Volume 56 (2008) no. 5, pp. 1206-1215 | DOI | MR | Zbl

[10] Vivian Hutson; Salomé Martínez; Konstantin Mischaikow; Glenn T. Vickers The evolution of dispersal, J. Math. Biol., Volume 47 (2003) no. 6, pp. 483-517 | DOI | MR | Zbl

[11] Liviu I. Ignat; Damián Pinasco; Julio D. Rossi; Angel San Antolín Decay estimates for nonlinear nonlocal diffusion problems in the whole space, J. Anal. Math., Volume 122 (2014), pp. 375-401 | DOI | MR | Zbl

[12] Liviu I. Ignat; Julio D. Rossi Asymptotic behaviour for a nonlocal diffusion equation on a lattice, Z. Angew. Math. Phys., Volume 59 (2008) no. 5, pp. 918-925 | DOI | MR | Zbl

[13] Stefan Kindermann; Stanley Osher; Peter W. Jones Deblurring and denoising of images by nonlocal functionals, Multiscale Model. Simul., Volume 4 (2005) no. 4, pp. 109-1115 | MR | Zbl

[14] Vangipuram Lakshmikantham; Drumi Dimitrov Bainov; e Pavel Sergeev Simeonov Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6, World Scientific, 1989 | MR | Zbl

[15] A Pazy Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, 44, Springer, 1983 | MR | Zbl

[16] Marcone C. Pereira; Julio D. Rossi Nonlocal problems in thin domains, J. Differ. Equations, Volume 263 (2017) no. 3, pp. 1725-1754 | DOI | MR | Zbl

[17] Marcone C. Pereira; Julio D. Rossi Nonlocal problems in perforated domains, Proc. R. Soc. Edinb., Sect. A, Math., Volume 150 (2020) no. 1, pp. 305-335 | DOI | MR | Zbl

[18] Mayte Pérez-Llanos; Julio D. Rossi Blow-up for a non-local diffusion problem with Neumann boundary conditions and a reaction term, Nonlinear Anal., Theory Methods Appl., Volume 70 (2009) no. 4, pp. 1629-1640 | DOI | MR | Zbl

[19] Aníbal Rodríguez-Bernal; Silvia Sastre-Gómez Nonlinear Nonlocal Reaction-Diffusion Equations, Advances in Differential Equations and Applications (SEMA SIMAI Springer Series), Volume 4, Springer, 2014, pp. 53-61 | DOI | MR | Zbl

[20] Aníbal Rodríguez-Bernal; Silvia Sastre-Gómez Linear nonlocal diffusion problems in metric measure spaces, Proc. R. Soc. Edinb., Sect. A, Math., Volume 146 (2016) no. 4, pp. 833-863 | DOI | Zbl

[21] Anatoliĭ Mykhaĭlovych Samoilenko; Nikolai A. Perestyuk Impulse Differential Equations, World Scientific Series on Nonlinear Science. Series A, 14, World Scientific, 1995 | Zbl

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