The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We...The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time T_M, with T_M in the interval [1, 2×3^(1/2)]/M for M > 0 and in the interval [2×2^(1/2), 2(1 +3^(1/2))]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time T_M employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L^2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.展开更多
By using the method of electrophoresis,three isozymes (lactate dehydrogenase,malate dehydrogenase and esterase) of three species of genus Gymnocypris were described and analyzed from North Tibet in this paper. The...By using the method of electrophoresis,three isozymes (lactate dehydrogenase,malate dehydrogenase and esterase) of three species of genus Gymnocypris were described and analyzed from North Tibet in this paper. The results showed that all three isozymes presented interspecific difference and distinct differentiation among individuals in the same population,and there was no electrophorectic difference between males and females. Analysis of relationships among three naked carps indicated a high degree of similarity between G. selincuoensis and G. cuoensis ,whereas low degree between G. selincuoensis and G. namensis . Furthermore,three isozymes presented expression of null alleles,and the duplicate genes of LDH A 2,LDH B 2,s MDH A 2 and m MDH B 2 also expressed in some individuals. Compared to other tetraploid fishes,three naked carps retained more functional duplicate genes and null alleles. This suggests fishes of genus Gymnocypris are at the early stage of evolution after polyploidization than that of fishes of Catostomidae,it directly related to the later time of schizothoracine fishes originate as well as severe environment.展开更多
In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced couple...In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.展开更多
文摘The advection-diffusion equation y_t~ε-εy_(xx)~ε+ M y_x~ε= 0,(x, t) ∈(0, 1) ×(0, T) is null controllable for any strictly positive values of the diffusion coefficient ε and of the controllability time T. We discuss here the behavior of the cost of control when the coefficient ε goes to zero, according to the values of T. It is actually known that this cost is uniformly bounded with respect to ε if T is greater than a minimal time T_M, with T_M in the interval [1, 2×3^(1/2)]/M for M > 0 and in the interval [2×2^(1/2), 2(1 +3^(1/2))]/|M | for M < 0. The exact value of TM is however unknown.We investigate in this work the determination of the minimal time T_M employing two distincts but complementary approaches. In a first one, we numerically estimate the cost of controllability, reformulated as the solution of a generalized eigenvalue problem for the underlying control operator, with respect to the parameter T and ε. This allows notably to exhibit the structure of initial data leading to large costs of control. At the practical level, this evaluation requires the non trivial and challenging approximation of null controls for the advection-diffusion equation. In the second approach, we perform an asymptotic analysis, with respect to the parameter ε, of the optimality system associated to the control of minimal L^2-norm. The matched asymptotic expansion method is used to describe the multiple boundary layers.
文摘By using the method of electrophoresis,three isozymes (lactate dehydrogenase,malate dehydrogenase and esterase) of three species of genus Gymnocypris were described and analyzed from North Tibet in this paper. The results showed that all three isozymes presented interspecific difference and distinct differentiation among individuals in the same population,and there was no electrophorectic difference between males and females. Analysis of relationships among three naked carps indicated a high degree of similarity between G. selincuoensis and G. cuoensis ,whereas low degree between G. selincuoensis and G. namensis . Furthermore,three isozymes presented expression of null alleles,and the duplicate genes of LDH A 2,LDH B 2,s MDH A 2 and m MDH B 2 also expressed in some individuals. Compared to other tetraploid fishes,three naked carps retained more functional duplicate genes and null alleles. This suggests fishes of genus Gymnocypris are at the early stage of evolution after polyploidization than that of fishes of Catostomidae,it directly related to the later time of schizothoracine fishes originate as well as severe environment.
文摘In this paper, the exact synchronization for a coupled system of wave equations with Dirichlet boundary controls and some related concepts are introduced. By means of the exact null controllability of a reduced coupled system, under certain conditions of compatibility, the exact synchronization, the exact synchronization by groups, and the exact null controllability and synchronization by groups are all realized by suitable boundary controls.
