The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping u_(tt)+u_(t)-div(a(u)u)=0,and show that,at least when n≥3,they tend,as t-+∞,to those of the nonlin...The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping u_(tt)+u_(t)-div(a(u)u)=0,and show that,at least when n≥3,they tend,as t-+∞,to those of the nonlinear parabolic equation v_t-div(a(v)v)=0,in the sense that the norm||u(.,t)-v(.,t)||_(L∞(R^n))of the difference u-v decays faster than that of either u or v.This provides another example of the diffusion phenomenon of nonlinear hyperbolic waves,first observed by Hsiao,L.and Liu Taiping(see[1,2]).展开更多
In this paper, the model of competing technologies diffusion was set up in order to analyze the relationship of competing technologies in diffusion process, and the stability of diffusion model with two kinds of compe...In this paper, the model of competing technologies diffusion was set up in order to analyze the relationship of competing technologies in diffusion process, and the stability of diffusion model with two kinds of competing technologies was analyzed. It is concluded that dominator can hold competing vantage by suppressing its opponent, and besides, whether competing technology can gain superiority in diffusion process depends on the success rates of technology diffusion when the two kinds of technology match each other in strength.展开更多
Parameter estimation plays a critical role for the application and development of S-shaped growth model in the agricultural sciences and others.In this paper,a modified particle swarm optimization algorithm based on t...Parameter estimation plays a critical role for the application and development of S-shaped growth model in the agricultural sciences and others.In this paper,a modified particle swarm optimization algorithm based on the diffusion phenomenon（DPPSO） was employed to estimate the parameters for this model.Under the sense of least squares,the parameter estimation problem of S-shaped growth model,taking the Gompertz and Logistic models for example,is transformed into a multi-dimensional function optimization problem.The results show that the DPPSO algorithm can effectively estimate the parameters of the S-shaped growth model.展开更多
文摘The authors consider the asymptotic behavior of solutions of the quasilinear hyperbolic equation with linear damping u_(tt)+u_(t)-div(a(u)u)=0,and show that,at least when n≥3,they tend,as t-+∞,to those of the nonlinear parabolic equation v_t-div(a(v)v)=0,in the sense that the norm||u(.,t)-v(.,t)||_(L∞(R^n))of the difference u-v decays faster than that of either u or v.This provides another example of the diffusion phenomenon of nonlinear hyperbolic waves,first observed by Hsiao,L.and Liu Taiping(see[1,2]).
文摘In this paper, the model of competing technologies diffusion was set up in order to analyze the relationship of competing technologies in diffusion process, and the stability of diffusion model with two kinds of competing technologies was analyzed. It is concluded that dominator can hold competing vantage by suppressing its opponent, and besides, whether competing technology can gain superiority in diffusion process depends on the success rates of technology diffusion when the two kinds of technology match each other in strength.
基金Supported by the National Natural Science Foundation of China (61070009)the National Science and Technology Support Plan (2012BAH25F02)+2 种基金the Project of Jingdezhen Science and Technology Bureau (2011-1-47)the National Natural Science Foundation of Jiangxi Province (2009GZS0065)the Youth Science Foundation of Jiangxi Provincial Department of Education (GJJ12514)
文摘Parameter estimation plays a critical role for the application and development of S-shaped growth model in the agricultural sciences and others.In this paper,a modified particle swarm optimization algorithm based on the diffusion phenomenon（DPPSO） was employed to estimate the parameters for this model.Under the sense of least squares,the parameter estimation problem of S-shaped growth model,taking the Gompertz and Logistic models for example,is transformed into a multi-dimensional function optimization problem.The results show that the DPPSO algorithm can effectively estimate the parameters of the S-shaped growth model.
