Stability analysis for impulsive stochastic fuzzy p-Laplace dynamic equations under Neumann or Dirichlet boundary condition

Under Neumann or Dirichlet boundary conditions, the stability of a class of delayed impulsive Markovian jumping stochastic fuzzy p -Laplace partial differential equations (PDEs) is considered. Thanks to some methods different from those of previous literature, the difficulties brought by fuzzy stoch...

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Bibliographic Details
Published inBoundary value problems Vol. 2013; no. 1; p. 133
Main Authors Rao, Ruofeng, Pu, Zhilin
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 20.05.2013
BioMed Central Ltd
Subjects
Analysis
Approximations and Expansions
Difference and Functional Equations
Mathematics
Mathematics and Statistics
Ordinary Differential Equations
Partial Differential Equations
Markovian jumping
Laplace diffusion
differential inequality
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Summary:Under Neumann or Dirichlet boundary conditions, the stability of a class of delayed impulsive Markovian jumping stochastic fuzzy p -Laplace partial differential equations (PDEs) is considered. Thanks to some methods different from those of previous literature, the difficulties brought by fuzzy stochastic mathematical model and impulsive model have been overcome. By way of the Lyapunov-Krasovskii functional, Itô formula, Dynkin formula and a differential inequality, new LMI-based global stochastic exponential stability criteria for the above-mentioned PDEs are established. Some applications of the obtained results improve some existing results on neural networks. And some numerical examples are presented to illustrate the effectiveness of the proposed method due to the significant improvement in the allowable upper bounds of time delays. MSC: 34D20, 34D23, 34B45, 34B37, 34K20.
ISSN:1687-2770
1687-2770
DOI:10.1186/1687-2770-2013-133