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Long-Time Behavior of a Stochastic Turbidostat Model Under degenerate diffusion

系统科学与复杂性学报:英文版 2023年第4期36卷 1641-1657页

作者： CAO Zhongwei MU Xiaojie JIANG Daqing Center for Teaching Faculty Development Jilin University of Finance and EconomicsChangchun 130117China School of Petroleum Engineering Key Laboratory of Unconventional Oil&Gas DevelopmentChina University of Petroleum(East China)Ministry of EducationQingdao 266580China College of Science China University of Petroleum(East China)Qingdao 266580China

Due to many uncertain factors,parameter values in many microorganism cultivation systems are affected to a greater or lesser extent by environmental *** this paper,the authors develop a stochastic turbidostat model that considers white noise,formulate and analyze dynamical behavior for the stochastic *** authors obtain the existence and uniqueness of globally positive *** conditions of the extinction for the system are *** the uniformly elliptic condition can fail to satisfy,the existence of the stationary distribution of the system is proved by using Markov semigroups *** speaking,the existence of stationary distribution suggests that microorganism will exist for a long *** analytical results are tested and verified by numerical simulations,which evaluate the influence of white noise on the dynamics of microorganism.

关键词： degenerate diffusion extinction markov semigroups stationary distribution stochastic turbidostat model

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CONVERGENCE OF NUMERICAL SCHEMES FOR A CONSERVATION EQUATION WITH CONVECTION AND degenerate diffusion

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Journal of Computational Mathematics 2021年第3期39卷 428-452页

作者： R.Eymard C.Guichard Xavier Lhebrard Universite Gustave Eiffel Laboratoire d'nalyse et de Mathematiques Appliquees(UMR 8050)UGEUPECCNRSF-77454Mame-la-ValleeFrance Sorbonne Universite Universite Paris-Diderot SPCCNRSInriaLaboratoire Jacques-Louis Lionsequipe ANGEF-75005 Paris Ecole Normale Superieure de Rennes France

The approximation of problems with linear convection and degenerate nonlinear diffusion,which arise in the framework of the transport of energy in porous media with thermodynamic transitions,is done usingθ-scheme based on the centred gradient discretisation *** convergence of the numerical scheme is proved,although the test functions which can be chosen are restricted by the weak regularity hypotheses on the convection field,owing to the application of a discrete Gronwall lemma and a general result for the time translate in the gradient discretisation *** numerical examples,using both the Control Volume Finite Element method and the Vertex Approximate Gradient scheme,show the role ofθfor stabilising the scheme.

关键词： Linear convection degenerate diffusion Gradient discretisation method θ-scheme

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ON MONOTONE TRAVELING WAVES FOR NICHOLSON'S BLOWFLIES EQUATION WITH degenerate p-LAPLACIAN diffusion

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Acta Mathematica Scientia 2024年第4期44卷 1550-1571页

作者： Rui HUANG Yong WANG Zhuo YIN School of Mathematical Sciences South China Normal UniversityGuangzhou 510631China

We study the existence and stability of monotone traveling wave solutions of Nicholson's blowflies equation with degenerate p-Laplacian *** prove the existence and nonexistence of non-decreasing smooth traveling wave solutions by phase plane analysis ***,we show the existence and regularity of an original solution via a compactness ***,we prove the stability and exponential convergence rate of traveling waves by an approximated weighted energy method.

关键词： degenerate diffusion p-Laplacian traveling waves stability

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HIGH RESOLUTION SCHEMES FOR CONSERVATION LAWS AND CONVECTION-diffusion EQUATIONS WITH VARYING TIME AND SPACE GRIDS

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Journal of Computational Mathematics 2006年第2期24卷 121-140页

作者： Hua-zhong Tang Gerald Warnecke LMAM School of Mathematical Sciences Peking University Beijing 100871 China Institut fiir Analysis und Numerik Otto-von-Guericke Universitat Magdeburg 39106 Magdeburg Germany

This paper presents a class of high resolution local time step schemes for nonlinear hyperbolic conservation laws and the closely related convection-diffusion equations, by projecting the solution increments of the underlying partial differential equations （PDE） at each local time step. The main advantages are that they are of good consistency, and it is convenient to implement them. The schemes are L^∞ stable, satisfy a cell entropy inequality, and may be extended to the initial boundary value problem of general unsteady PDEs with higher-order spatial derivatives. The high resolution schemes are given by combining the reconstruction technique with a second order TVD Runge-Kutta scheme or a Lax-Wendroff type method, respectively. The schemes are used to solve a linear convection-diffusion equation, the nonlinear inviscid Burgers＇ equation, the one- and two-dimensional compressible Euler equations, and the two-dimensional incompressible Navier-Stokes equations. The numerical results show that the schemes are of higher-order accuracy, and efficient in saving computational cost, especially, for the case of combining the present schemes with the adaptive mesh method [15]. The correct locations of the slow moving or stronger discontinuities are also obtained, although the schemes are slightly nonconservative.

关键词： Hyperbolic conservation laws degenerate diffusion High resolution scheme,Finite volume method Local time discretization.

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