Parameter identification of nonlinear delayed dynamical system in microbial fermentation based on biological robustness
Lei Wang Jinlong Yuan Yingfang Li Enmin Feng Zhilong Xiu
Numerical Algebra, Control & Optimization 2014, 4(2): 103-113 doi: 10.3934/naco.2014.4.103
In this paper, the nonlinear enzyme-catalytic kinetic system of batch and continuous fermentation in the process of glycerol bio-dissimilation is investigated. On the basis of both glycerol and 1,3-PD pass the cell membrane by active and passive diffusion under substrate-sufficient conditions, we consider the delay of concentration changes on both extracellular substances and intracellular substances. We establish a nonlinear delay dynamical system according to the batch and continuous fermentation of bio-dissimilation of glycerol to 1,3-propanediol(1,3-PD) and we propose an identification problem, in which the biological robustness is taken as a performance index, constrained with nonlinear delay dynamical system. An algorithm is constructed to solve the identification problem and the numerical result shows the values of time delays of glycerol, 3-HPA, 1,3-PD intracellular and extracellular substances. This work will be helpful for deeply understanding the metabolic mechanism of glycerol in batch and continuous fermentation.
keywords: biological robustness parameter identification Nonlinear time-delay system continuous and batch fermentation.
Stochastic maximum principle for partial information optimal investment and dividend problem of an insurer
Yan Wang Yanxiang Zhao Lei Wang Aimin Song Yanping Ma
Journal of Industrial & Management Optimization 2018, 14(2): 653-671 doi: 10.3934/jimo.2017067

We study an optimal investment and dividend problem of an insurer, where the aggregate insurance claims process is modeled by a pure jump Lévy process. We allow the management of the dividend payment policy and the investment of surplus in a continuous-time financial market, which is composed of a risk free asset and a risky asset. The information available to the insurer is partial information. We generalize this problem as a partial information regular-singular stochastic control problem, where the control variable consists of regular control and singular control. Then maximum principles are established to give sufficient and necessary optimality conditions for the solutions of the regular-singular control problem. Finally we apply the maximum principles to solve the investment and dividend problem of an insurer.

keywords: Optimal investment dividend insurance claim process maximum principle regular-singular stochastic control partial information
Parameter identification and numerical simulation for the exchange coefficient of dissolved oxygen concentration under ice in a boreal lake
Qinxi Bai Zhijun Li Lei Wang Bing Tan Enmin Feng
Journal of Industrial & Management Optimization 2018, 14(4): 1463-1478 doi: 10.3934/jimo.2018016

Dissolved oxygen (DO) is one of the main parameters to assess the quality of lake water. This study is intended to construct a parabolic distributed parameter system to describe the variation of DO under the ice, and identify the vertical exchange coefficient K of DO with the field data. Based on the existence and uniqueness of the weak solution of this system, the fixed solution problem of the parabolic equation is transformed into a parameter identification model, which takes K as the identification parameter, and the deviation of the simulated and measured DO as the performance index. We prove the existence of the optimal parameter of the identification model, and derive the first order optimality conditions. Finally, we construct the optimization algorithm, and have carried out numerical simulation. According to the measured DO data in Lake Valkea-Kotinen (Finland), it can be found that the orders of magnitude of the coefficient K varying from 10-6 to 10-1 m2 s-1, the calculated and measured DO values are in good agreement. Within this range of K values, the overall trends are very similar. In order to get better fitting, the formula needs to be adjusted based on microbial and chemical consumption rates of DO.

keywords: Dissolved oxygen parameter identification numerical simulation partial differential equation frozen lakes
Renormalized entropy solutions for degenerate parabolic-hyperbolic equations with time-space dependent coefficients
Zhigang Wang Lei Wang Yachun Li
Communications on Pure & Applied Analysis 2013, 12(3): 1163-1182 doi: 10.3934/cpaa.2013.12.1163
We study the well-posedness of renormalized entropy solutions to the Cauchy problem for general degenerate parabolic-hyperbolic equations of the form \begin{eqnarray*} \partial_{t}u+ \sum_{i=1}^{d}\partial_{x_{i}f_{i}(u,t,x)}= \sum_{i,j=1}^{d}\partial_{x_j}(a_{ij}(u,t,x)\partial_{x_i}u)+\gamma(t,x) \end{eqnarray*} with initial data $u(0,x)=u_{0}(x)$, where the convection flux function $f$, the diffusion function $a$, and the source term $\gamma$ depend explicitly on the independent variables $t$ and $x$. We prove the uniqueness by using Kružkov's device of doubling variables and the existence by using vanishing viscosity method.
keywords: device of doubling variables Degenerate parabolic-hyperbolic equation vanishing viscosity method. renormalized entropy solutions entropy solutions

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