pth moment exponential stability of hybrid stochastic fourth-order parabolic equations

Ling, Wei; Zhu, Quanxin; Duan, Mianjun; Yao, Zhangsong

doi:10.1186/s13662-016-0781-y

Cited by 3 publications

(1 citation statement)

References 10 publications

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“…In recent years, stochastic parabolic partial differential equations have received a great deal of attention due to their important applications in biological, control engineering, economics, physics, social sciences, and so on. Hence, the theory of stochastic parabolic partial differential equations has developed very quickly [1][2][3]. On the other hand, in many realistic models, their future states depend not only on the present states but also on the past ones.…”

Section: Introductionmentioning

confidence: 99%

Convergence and stability of stochastic parabolic functional differential equations

2018

Adv Differ Equ

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The main purpose of this paper is to investigate the convergence and stability of stochastic parabolic functional differential equations. Firstly, a comparison theorem in the context of Lyapunov-like function together with differential inequality is established. Secondly, various criteria for the convergence and stability are obtained on the basis of the comparison theorem and stochastic analysis techniques. Finally, two examples are provided to illustrate the significance of the theoretical results.

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Section: Introductionmentioning

confidence: 99%

Convergence and stability of stochastic parabolic functional differential equations

2018

Adv Differ Equ

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Numerical Bifurcation Analysis of Physiologically Structured Population Models via Pseudospectral Approximation

et al. 2020

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We propose an approximation of nonlinear renewal equations by means of ordinary differential equations. We consider the integrated state, which is absolutely continuous and satisfies a delay differential equation. By applying the pseudospectral approach to the abstract formulation of the differential equation, we obtain an approximating system of ordinary differential equations. We present convergence proofs for equilibria and the associated characteristic roots, and we use some models from ecology and epidemiology to illustrate the benefits of the approach to perform numerical bifurcation analyses of equilibria and periodic solutions. The numerical simulations show that the implementation of the new approximating system is ten times more efficient than the one originally proposed in [Breda et al, SIAM Journal on Applied Dynamical Systems, 2016], as it avoids the numerical inversion of an algebraic equation.

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Construction of global solutions for a symmetric system of Keyfitz–Kranzer type with three piecewise constant states

2019

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The exact solutions of the Riemann problem for a symmetric system of Keyfitz-Kranzer type are obtained in fully explicit forms. Furthermore, the global solutions of the double Riemann problems are also constructed explicitly when the initial data are taken to be three piecewise constant states. During the process of constructing the global solutions, all occurring wave interactions have been dealt with in detail by using the method of characteristics. In addition, it is shown that the Riemann solutions are stable with respect to the specific small perturbations of the Riemann initial data.

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pth moment exponential stability of hybrid stochastic fourth-order parabolic equations

Cited by 3 publications

References 10 publications

Convergence and stability of stochastic parabolic functional differential equations

Convergence and stability of stochastic parabolic functional differential equations

Numerical Bifurcation Analysis of Physiologically Structured Population Models via Pseudospectral Approximation

Construction of global solutions for a symmetric system of Keyfitz–Kranzer type with three piecewise constant states

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