ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS∗

doi:10.1007/s10473-023-0424-9

Abstract

Abstract: This paper focuses on the analytical and numerical asymptotical stability of neutral reaction-diffusion equations with piecewise continuous arguments. First, for the analytical solutions of the equations, we derive their expressions and asymptotical stability criteria. Second, for the semi-discrete and one-parameter fully-discrete finite element methods solving the above equations, we work out the sufficient conditions for assuring that the finite element solutions are asymptotically stable. Finally, with a typical example with numerical experiments, we illustrate the applicability of the obtained theoretical results.

Key words: neutral reaction-diffusion equations, piecewise continuous arguments, asymptotical stability, finite element methods, numerical experiment

Hao HAN, Chengjian ZHANG. ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS^∗[J].Acta mathematica scientia,Series B, 2023, 43(4): 1865-1880.

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ASYMPTOTICAL STABILITY OF NEUTRAL REACTION-DIFFUSION EQUATIONS WITH PCAS AND THEIR FINITE ELEMENT METHODS^∗

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