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Journal of Systems Science & Complexity 2015年第5期28卷 1033-1048页

作者： PALANISAMY Muthukumar CHINNATHAMBI Rajivganthi Department of Mathematics Gandhigram Rural Institute-Deemed University

The modelling of risky asset by stochastic processes with continuous paths, based on Brownian motions, suffers from several defects. First, the path continuity assumption does not seem reasonable in view of the possibility of sudden price variations(jumps) resulting of market crashes. A solution is to use stochastic processes with jumps, that will account for sudden variations of the asset prices. On the other hand, such jump models are generally based on the Poisson random measure. Many popular economic and financial models described by stochastic differential equations with Poisson jumps. This paper deals with the approximate controllability of a class of second-order neutral stochastic differential equations with infinite delay and Poisson jumps. By using the cosine family of operators, stochastic analysis techniques, a new set of sufficient conditions are derived for the approximate controllability of the above control system. An example is provided to illustrate the obtained theory.

关键词： Approximate controllability Hilbert space Poisson jumps second-order neutral stochastic differential equations semigroup theory

Controllability results for nonlinear impulsive integrodifferential evolution systems with time-varying delays

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控制理论与应用（英文版） 2013年第3期11卷 415-421页

作者： Bheeman RADHAKRISHNAN Krishnan BALACHANDRAN Department of Applied Mathematics & Computational Sciences PSG College of Technology Department of Mathematics Bharathiar University

In this paper, we study the controllability results for the nonlinear impulsive integrodifferential evolution systems with time-varying delays in Banach spaces. The sufficient conditions of exact controllability is proved under without assuming the compactness of the evolution operator. The results are obtained by using the semigroup theory and the Schafer fixed point theorem.

关键词： Controllability Impulsive integrodifferential system Evolution operator Time varying delay Fixed point theorem semigroup theory

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Controllability results for semilinear impulsive integrodifferential evolution systems with nonlocal conditions

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控制理论与应用（英文版） 2012年第1期10卷 28-34页

作者： Bheeman RADHAKRISHNAN Krishnan BALACHANDRAN Department of Mathematics Bharathiar University

In this paper, we establish sufficient conditions for the controllability of a class of semilinear impulsive integrodifferential systems with nonlocal initial conditions in Banach spaces. We derive the conditions using Hausdorff measure of noncompactness, Sadovskii fixed point theorem and operator semigroups in particular dropping compactness of the operator.

关键词： Controllability Impulsive integrodifferential system Evolution operator Nonlocal initial conditions Condensing operator Sadovskii fixed point theorem semigroup theory

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Approximate controllability of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces

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控制理论与应用（英文版） 2013年第3期11卷 351-358页

作者： P.MUTHUKUMAR C.RAJIVGANTHI Department of Mathematics Gandhigram Rural Institute-Deemed University

Many practical systems in physical and technical sciences have impulsive dynamical behaviors during the evolution process which can be modeled by impulsive differential equations. In this paper, we prove the approximate controllability of control systems governed by a class of impulsive neutral stochastic functional differential system with state-dependent delay in Hilbert spaces. Sufficient conditions for approximate controllability of the control systems are established under the natural assumption that the corresponding linear system is approximately controllable. The results are obtained by using semigroup theory, stochastic analysis techniques, fixed point approach and abstract phase space axioms. An example is provided to illustrate the application of the obtained results.

关键词： Approximate controllability Hilbert space Impulsive neutral stochastic functional differential system semigroup theory Sadovskii’s fixed point theorem

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Mathematical Analysis of the Jin-Neelin Model of El Nio-Southern-Oscillation

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 1-38页

作者： Yining CAO Mickaёl D.CHEKROUN Aimin HUANG Roger TEMAM Department of Mathematics and the Institute for Scientific Computing and Applied Mathematics Indiana University Department of Atmospheric and Oceanic Sciences University of California

The Jin-Neelin model for the El Nio–Southern Oscillation(ENSO for short) is considered for which the authors establish existence and uniqueness of global solutions in time over an unbounded channel domain. The result is proved for initial data and forcing that are sufficiently small. The smallness conditions involve in particular key physical parameters of the model such as those that control the travel time of the equatorial waves and the strength of feedback due to vertical-shear currents and upwelling; central mechanisms in ENSO dynamics.From the mathematical view point, the system appears as the coupling of a linear shallow water system and a nonlinear heat equation. Because of the very different nature of the two components of the system, the authors find it convenient to prove the existence of solution by semi-discretization in time and utilization of a fractional step scheme. The main idea consists of handling the coupling between the oceanic and temperature components by dividing the time interval into small sub-intervals of length k and on each sub-interval to solve successively the oceanic component, using the temperature T calculated on the previous sub-interval, to then solve the sea-surface temperature(SST for short) equation on the current sub-interval. The passage to the limit as k tends to zero is ensured via a priori estimates derived under the aforementioned smallness conditions.

关键词： El Nio–Southern Oscillation Coupled nonlinear hyperbolic-parabolic systems Fractional step method semigroup theory

Mathematical Analysis of the Jin-Neelin Model of El Niño-Southern-Oscillation

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Chinese Annals of Mathematics,Series B 2019年第1期40卷 1-38页

关键词： El Niño-Southern Oscillation Coupled nonlinear hyperbolic-parabolic systems Fractional step method semigroup theory

Asymptotic Stability of Singular Solution for Camassa-Holm Equation

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Journal of Applied Mathematics and Physics 2021年第7期9卷 1505-1514页

作者： Yuetian Gao School of Mathematics and Computer Science Yunnan Minzu University Kunming China

The aim of this paper is to study singular dynamics of solutions of Camassa-Holm equation. Based on the semigroup theory of linear operators and Banach contraction mapping principle, we prove the asymptotic stability ... 详细信息

关键词： Asymptotic Stability Camassa-Holm Equation Explicit Solution semigroup theory Banach Contraction Mapping Principle