Through this paper we deal with the asymptotic behaviour as 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.
Révisé le :
Accepté le :
Publié le :
@article{CRMATH_2020__358_11-12_1119_0, author = {Ferreira, Jaqueline da Costa and Pereira, Marcone Corr\^ea}, title = {A nonlocal {Dirichlet} problem with impulsive action: estimates of the growth for the solutions}, journal = {Comptes Rendus. Math\'ematique}, pages = {1119--1128}, publisher = {Acad\'emie des sciences, Paris}, volume = {358}, number = {11-12}, year = {2020}, doi = {10.5802/crmath.109}, language = {en}, url = {http://www.numdam.org/articles/10.5802/crmath.109/} }
TY - JOUR AU - Ferreira, Jaqueline da Costa AU - Pereira, Marcone Corrêa TI - A nonlocal Dirichlet problem with impulsive action: estimates of the growth for the solutions JO - Comptes Rendus. Mathématique PY - 2020 SP - 1119 EP - 1128 VL - 358 IS - 11-12 PB - Académie des sciences, Paris UR - http://www.numdam.org/articles/10.5802/crmath.109/ DO - 10.5802/crmath.109 LA - en ID - CRMATH_2020__358_11-12_1119_0 ER -
%0 Journal Article %A Ferreira, Jaqueline da Costa %A Pereira, Marcone Corrêa %T A nonlocal Dirichlet problem with impulsive action: estimates of the growth for the solutions %J Comptes Rendus. Mathématique %D 2020 %P 1119-1128 %V 358 %N 11-12 %I Académie des sciences, Paris %U http://www.numdam.org/articles/10.5802/crmath.109/ %R 10.5802/crmath.109 %G en %F CRMATH_2020__358_11-12_1119_0
Ferreira, Jaqueline da Costa; Pereira, Marcone Corrêa. A nonlocal Dirichlet problem with impulsive action: estimates of the growth for the solutions. Comptes Rendus. Mathématique, Tome 358 (2020) no. 11-12, pp. 1119-1128. doi : 10.5802/crmath.109. http://www.numdam.org/articles/10.5802/crmath.109/
[1] 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] Travelling waves in a convolution model for phase transitions, Arch. Ration. Mech. Anal., Volume 138 (1997) no. 2, pp. 105-136 | DOI | Zbl
[3] Remarks on the spectrum of a nonlocal Dirichlet problem (2019) (https://arxiv.org/abs/1911.05803v3)
[4] 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] 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] 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] 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] On the principal eigenvalue of some nonlocal diffusion problems, J. Differ. Equations, Volume 246 (2009) no. 1, pp. 21-38 | DOI | MR | Zbl
[9] Global solutions for impulsive abstract partial differential equations, Comput. Math. Appl., Volume 56 (2008) no. 5, pp. 1206-1215 | DOI | MR | Zbl
[10] The evolution of dispersal, J. Math. Biol., Volume 47 (2003) no. 6, pp. 483-517 | DOI | MR | Zbl
[11] Decay estimates for nonlinear nonlocal diffusion problems in the whole space, J. Anal. Math., Volume 122 (2014), pp. 375-401 | DOI | MR | Zbl
[12] 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] Deblurring and denoising of images by nonlocal functionals, Multiscale Model. Simul., Volume 4 (2005) no. 4, pp. 109-1115 | MR | Zbl
[14] Theory of impulsive differential equations, Series in Modern Applied Mathematics, 6, World Scientific, 1989 | MR | Zbl
[15] Semigroups of linear operators and applications to partial differential equations, Applied Mathematical Sciences, 44, Springer, 1983 | MR | Zbl
[16] Nonlocal problems in thin domains, J. Differ. Equations, Volume 263 (2017) no. 3, pp. 1725-1754 | DOI | MR | Zbl
[17] Nonlocal problems in perforated domains, Proc. R. Soc. Edinb., Sect. A, Math., Volume 150 (2020) no. 1, pp. 305-335 | DOI | MR | Zbl
[18] 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] 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] 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] Impulse Differential Equations, World Scientific Series on Nonlinear Science. Series A, 14, World Scientific, 1995 | Zbl
Cité par Sources :