With fast increase in aquaculture, there comes the environmental problems which have received most attentions. The pollution from aquaculture includes nitrogen and phosphorus loading, unexpected chemicals and organism...With fast increase in aquaculture, there comes the environmental problems which have received most attentions. The pollution from aquaculture includes nitrogen and phosphorus loading, unexpected chemicals and organisms. Poor water environment not only resulted in poor growth efficiency of fish, but also in poor fish quality and high risk of diseases.展开更多
This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantia...This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantially different from the closely related works,and have zero-dynamics,unknown growth rate,and unknown time-varying control coefficients.This makes the problem much more difficult to solve.Motivated by the authors' recent works,this paper proposes a new adaptive control scheme to achieve the global practical tracking.It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time.This is achieved by combining the methods of universal control and dead zone with backstepping technique,and using the framework of performance analysis in the closely related works.A numerical example demonstrates the effectiveness of the theoretical results.展开更多
This paper deals with the existence of solutions for the problem{（Фp（u′））′=f（t,u,u′）,t∈（0,1）, u′（0）=0,u（1）=∑i=1^n-2aiu（ηi）,where Фp（s）=｜s｜^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai（i=1,2,…,n-...This paper deals with the existence of solutions for the problem{（Фp（u′））′=f（t,u,u′）,t∈（0,1）, u′（0）=0,u（1）=∑i=1^n-2aiu（ηi）,where Фp（s）=｜s｜^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai（i=1,2,…,n-2）are non-negative constants and ∑i=1^n-2ai=1.Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory.展开更多
To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been ...To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.展开更多
This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a ...This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.展开更多
In this paper, a free boundary problem for a solid avascular tumor growth under the action of periodic external inhibitors with time delays in proliferation is studied. Suffi- cient conditions for the global stability...In this paper, a free boundary problem for a solid avascular tumor growth under the action of periodic external inhibitors with time delays in proliferation is studied. Suffi- cient conditions for the global stability of tumor-free equilibrium are given. Moreover, if external concentration of nutrients is large, we also prove that the tumor will not disappear and determine the conditions under which there exist periodic solutions to the model. The results show that the periodicity of the inhibitor may imply periodicity of the size of the tumor. More precisely, if aoc （the concentration of external nutrients） is greater than μβ ＋ , where μ, v are two constants; β＊ = max0≤t≤ωФ（t）; Ф（t） is a periodic function which can be interpreted as a treatment and w is the period of Ф（t）. Results are illustrated by computer simulations.展开更多
文摘With fast increase in aquaculture, there comes the environmental problems which have received most attentions. The pollution from aquaculture includes nitrogen and phosphorus loading, unexpected chemicals and organisms. Poor water environment not only resulted in poor growth efficiency of fish, but also in poor fish quality and high risk of diseases.
基金supported by the National Natural Science Foundation of China under Grant Nos.61325016,61273084,61233014,and 61304013the Natural Science Foundation for Distinguished Young Scholar of Shandong Province of China under Grant No.JQ200919+1 种基金the Independent Innovation Foundation of Shandong University under Grant No.2012JC014the Doctoral Foundation of Jinan University under Grant No.XBS1413
文摘This paper deals with the global practical tracking problem by output-feedback for a class of uncertain cascade systems with zero-dynamics and unmeasured states dependent growth.The systems investigated are substantially different from the closely related works,and have zero-dynamics,unknown growth rate,and unknown time-varying control coefficients.This makes the problem much more difficult to solve.Motivated by the authors' recent works,this paper proposes a new adaptive control scheme to achieve the global practical tracking.It is shown that the designed controller guarantees that the state of the resulting closed-loop system is globally bounded and the tracking error converges to a prescribed arbitrarily small neighborhood of the origin after a finite time.This is achieved by combining the methods of universal control and dead zone with backstepping technique,and using the framework of performance analysis in the closely related works.A numerical example demonstrates the effectiveness of the theoretical results.
基金the National Natural Science Foundation of China(No.10771212)the Foundation of China University of Mining and Technology(Nos.2005A041+1 种基金2006A0422008A037)
文摘This paper deals with the existence of solutions for the problem{（Фp（u′））′=f（t,u,u′）,t∈（0,1）, u′（0）=0,u（1）=∑i=1^n-2aiu（ηi）,where Фp（s）=｜s｜^p-2s,p〉1.0〈η1〈η2〈…〈ηn-2〈1,ai（i=1,2,…,n-2）are non-negative constants and ∑i=1^n-2ai=1.Some known results are improved under some sign and growth conditions. The proof is based on the Brouwer degree theory.
基金This work was partially supported by the National Natural Science Foundation of China （11771381） and Project funded by China Postdoctoral Science Foundation.
文摘To understand the impact of environmental heterogeneity and mutualistic interaction of species, we consider a mutualistic model with cross-diffusion in a heterogeneous environ- ment. Semi-coexistence states have been studied by using the corresponding eigenvalue problems, and sufficient conditions for the existence and non-existence of coexistence states are given. Our results show that the model possesses at least one coexistence solution if the intrinsic populations growth rates are big or free-diffusion and cross-diffusion coefficients are weak. Otherwise, the model have no coexistence solution. The true solutions are obtained by utilizing the monotone iterative schemes. In order to illustrate our analytical results, some numerical simulations are given.
文摘This paper deals with the homogenization of a class of nonlinear elliptic problems with quadratic growth in a periodically perforated domain. The authors prescribe a Dirichlet condition on the exterior boundary and a nonhomogeneous nonlinear Robin condition on the boundary of the holes. The main difficulty, when passing to the limit, is that the solution of the problems converges neither strongly in L^2(Ω) nor almost everywhere in Ω. A new convergence result involving nonlinear functions provides suitable weak convergence results which permit passing to the limit without using any extension operator.Consequently, using a corrector result proved in [Chourabi, I. and Donato, P., Homogenization and correctors of a class of elliptic problems in perforated domains, Asymptotic Analysis, 92(1), 2015, 1–43, DOI: 10.3233/ASY-151288], the authors describe the limit problem, presenting a limit nonlinearity which is different for the two cases, that of a Neumann datum with a nonzero average and with a zero average.
文摘In this paper, a free boundary problem for a solid avascular tumor growth under the action of periodic external inhibitors with time delays in proliferation is studied. Suffi- cient conditions for the global stability of tumor-free equilibrium are given. Moreover, if external concentration of nutrients is large, we also prove that the tumor will not disappear and determine the conditions under which there exist periodic solutions to the model. The results show that the periodicity of the inhibitor may imply periodicity of the size of the tumor. More precisely, if aoc （the concentration of external nutrients） is greater than μβ ＋ , where μ, v are two constants; β＊ = max0≤t≤ωФ（t）; Ф（t） is a periodic function which can be interpreted as a treatment and w is the period of Ф（t）. Results are illustrated by computer simulations.
