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Zbl 1160.35448
Zhu, Wei
Global exponential stability of impulsive reaction-diffusion equation with variable delays. (English)
[J] Appl. Math. Comput. 205, No. 1, 362-369 (2008). ISSN 0096-3003

Summary: The global exponential stability of an impulsive reaction-diffusion equation with variable delays is investigated. By establishing an impulsive differential inequality and using the propertied of $\rho $-cone and eigenspace of the spectral radius of nonnegative matrix, some new sufficient conditions on its global exponential stability are obtained. The sufficient conditions are easily checked in practice by simple algebra methods and have a wider adaptive range. An example is given to illustrate the effectiveness of the theoretical result.

MSC 2000:: *35K57 Reaction-diffusion equations
35R12 Impulsive partial differential equations
35B35 Stability of solutions of PDE

Keywords: global exponential stability; reaction-diffusion; impulsive; impulsive differential inequality; spectral radius

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Zentralblatt MATH Berlin [Germany]