Dynamical Behavior of Nonlinear Impulsive Abstract Partial Differential Equations on Networks with Multiple Time-Varying Delays and Mixed Boundary Conditions Involving Time-Varying Delays - Université de Rennes Accéder directement au contenu
Article Dans Une Revue Journal of Dynamical and Control Systems Année : 2015

Dynamical Behavior of Nonlinear Impulsive Abstract Partial Differential Equations on Networks with Multiple Time-Varying Delays and Mixed Boundary Conditions Involving Time-Varying Delays

Résumé

Various real-world problems in physics, biology, neuroscience, communicationand transport networks, engineering science, and so on, subject to abrupt changes at certaininstants during the dynamical processes, can be well-described by impulsive partialdifferential equations on networks with time-varying delays. The purpose of this paper isto investigate the existence, stability, and global attractivity of a class of coupled impulsivesystem of nonlinear reaction-diffusion type equations on networks in which different timevaryingdelays appear both in the nonlinear reaction functions and in the mixed boundaryconditions. The problem under consideration can be included coupled systems of reactiondiffusionand ordinary differential equations. By using the method of upper and lowersolutions and its associated monotone iterations, the existence-uniqueness of the solution,the stability and attractivity analysis for quasi-monotone nondecreasing and mixed quasimonotonereaction and impulsive functions, are considered. The results for the generalsystem are applied to the standard PDE reaction-diffusion system without time delaysand/or impulsive behavior and to the corresponding ordinary differential system. To illustratethe abstract results, problems of three-species food-chain reaction-diffusion modelswith time-varying delays and impulsive perturbations are considered.
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Dates et versions

hal-01113057 , version 1 (04-02-2015)

Identifiants

Citer

Aziz Belmiloudi. Dynamical Behavior of Nonlinear Impulsive Abstract Partial Differential Equations on Networks with Multiple Time-Varying Delays and Mixed Boundary Conditions Involving Time-Varying Delays. Journal of Dynamical and Control Systems, 2015, 21 (1), pp.95-146. ⟨10.1007/s10883-014-9230-y⟩. ⟨hal-01113057⟩
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