In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The...In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.展开更多
The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of ...The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different 'thickness', the N-order approximate expansion of perturbed solution concerning small parameter is obtained, and the 'multiple layer' phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.展开更多
The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourie...The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.展开更多
A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalitie...A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied.展开更多
We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and il...We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t = 0. The strong convergence results only hold outside the initial layer.展开更多
We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that...We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.展开更多
Recognizing the nature and formation progress of the ash deposits is essential to resolve the deposition problem hindering the wide application of large-scale biomass-fired boilers.Therefore,the ash deposits in the su...Recognizing the nature and formation progress of the ash deposits is essential to resolve the deposition problem hindering the wide application of large-scale biomass-fired boilers.Therefore,the ash deposits in the superheaters of a 220 t/h biomass-fired CFB boiler were studied,including the platen(PS),the high-temperature(HTS),the upper and the lower low-temperature superheaters(LTS).The results showed that the deposits in the PSs and HTSs were thin(several millimeters)and compact,consisting of a yellow outer layer and snow-white inner layer near the tube surface.The deposits in the upper LTS appeared to be toughly sintered ceramic,while those in the lower LTS were composed of dispersive coarse ash particles with an unsintered surface.Detailed characterization of the cross-section and the initial layers in the deposits revealed that the dominating compositions in both the PSs and the HTSs were Cl and K(approximately 70%)in the form of KCl.Interestingly,the cross-section of the deposition in the upper LTS exhibited a unique lamellar structure with a major composition of Ca and S.The contents of Ca and Si increased from approximately 10%to approximately 60%in the deposits from the high temperature surfaces to the low temperature ones.It was concluded that the vaporized mineral matter such as KCl played the most important role in the deposition progress in the PS and the HTS.In addition,although the condensation of KCl in the LTSs also happened,the deposition of ash particles played a more important role.展开更多
In this paper we consider the relaxation limits of the two-fluid Euler-Maxwellsystems with initial layer. We construct an asymptotic expansion with initial layerfunctions and prove the convergence between the exact so...In this paper we consider the relaxation limits of the two-fluid Euler-Maxwellsystems with initial layer. We construct an asymptotic expansion with initial layerfunctions and prove the convergence between the exact solutions and the approximatesolutions.展开更多
文摘In this article we study quasi-neutral limit and the initial layer problem of the drift-diffusion model.Different from others studies,we consider the physical case that the mobilities of the charges are different..The quasi-neutral limit with an initial layer structure is rigorously proved by using the weighted energy method coupled with multi-scaling asymptotic expansions.
文摘The initial layer phenomena for a class of singular perturbed nonlinear system with slow variables are studied. By introducing stretchy variables with different quantity levels and constructing the correction term of initial layer with different 'thickness', the N-order approximate expansion of perturbed solution concerning small parameter is obtained, and the 'multiple layer' phenomena of perturbed solutions are revealed. Using the fixed point theorem, the existence of perturbed solution is proved, and the uniformly valid asymptotic expansion of the solutions is given as well.
基金partial supported by the National Natural Science Foundation of China(Grant Nos.71774073,71988101)Social Scienceof Jiangxi Provincial(Grant No.20YJ02)+1 种基金Natural Science Foundation of Jiangxi Provincial(Grant No.20171BAA208019)partial supported by Jiangxi Provincial Department of Education Science and Technology Research Project(GJJ213110)。
文摘The paper deals with a Cauchy problem for the chemotaxis system with the effect of fluid■where d≥2.It is known that for each∈>0 and all sufficiently small initial data(u_(0),n_(0),c_(0))belongs to certain Fourier space,the problem possesses a unique global solution(u^(∈),n^(∈),c^(∈))in Fourier space.The present work asserts that these solutions stabilize to(u^(∞),n^(∞),c^(∞))as∈^(-1)→0.Moreover,we show that c^(∈)(t)has the initial layer as∈^(-1)→0.As one expects its limit behavior maybe give a new viewlook to understand the system.
基金supported by the National Natural Science Foundation of China (Nos.40676016,40876010)the Key Innovation Project of the Chinese Academy of Sciences (No.KZCX2-YW-Q03-08)the E-Institute of Shanghai Municipal Education Commission (No. E03004)
文摘A class of singularly perturbed initial boundary value problems for semilinear reaction diffusion equations with two parameters is considered, Under suitable conditions and using the theory of differential inequalities, the existence and the asymptotic behavior of the solution to the initial boundary value problem are studied.
基金supported by Postdoctoral Science Foundation of China through Grant 2017M610818
文摘We are concerned with the zero dielectric constant limit for the full electromagneto-fluid dynamics in this article. This singular limit is justified rigorously for global smooth solution for both well-prepared and ill-prepared initial data. The explicit convergence rate is also obtained by a elaborate energy estimate. Moreover, we show that for the wellprepared initial data, there is no initial layer, and the electric field always converges strongly to the limit function. While for the ill-prepared data case, there will be an initial layer near t = 0. The strong convergence results only hold outside the initial layer.
基金supported by National Natural Science Foundation of China(Grant Nos.11226170,10976026 and 11271305)China Postdoctoral Science Foundation Funded Project(Grant No.2012M511640)+1 种基金Hunan Provincial Natural Science Foundation of China(Grant No.13JJ4095)National Science Foundation of USA(Grant Nos.DMS-0807406 and DMS-1108994)
文摘We investigate the zero dissipation limit problem of the one-dimensional compressible isentropic Navier-Stokes equations with Riemann initial data in the case of the composite wave of two shock waves. It is shown that the unique solution to the Navier-Stokes equations exists for all time, and converges to the Riemann solution to the corresponding Euler equations with the same Riemann initial data uniformly on the set away from the shocks, as the viscosity vanishes. In contrast to previous related works, where either the composite wave is absent or the effects of initial layers are ignored, this gives the first mathematical justification of this limit for the compressible isentropic Navier-Stokes equations in the presence of both composite wave and initial layers. Our method of proof consists of a scaling argument, the construction of the approximate solution and delicate energy estimates.
基金This work was supported by the National Natural Science Foundation of China(Grant Nos.51806075 and 51922045),and the Analytical and Testing Center of Huazhong University of Science and Technology.
文摘Recognizing the nature and formation progress of the ash deposits is essential to resolve the deposition problem hindering the wide application of large-scale biomass-fired boilers.Therefore,the ash deposits in the superheaters of a 220 t/h biomass-fired CFB boiler were studied,including the platen(PS),the high-temperature(HTS),the upper and the lower low-temperature superheaters(LTS).The results showed that the deposits in the PSs and HTSs were thin(several millimeters)and compact,consisting of a yellow outer layer and snow-white inner layer near the tube surface.The deposits in the upper LTS appeared to be toughly sintered ceramic,while those in the lower LTS were composed of dispersive coarse ash particles with an unsintered surface.Detailed characterization of the cross-section and the initial layers in the deposits revealed that the dominating compositions in both the PSs and the HTSs were Cl and K(approximately 70%)in the form of KCl.Interestingly,the cross-section of the deposition in the upper LTS exhibited a unique lamellar structure with a major composition of Ca and S.The contents of Ca and Si increased from approximately 10%to approximately 60%in the deposits from the high temperature surfaces to the low temperature ones.It was concluded that the vaporized mineral matter such as KCl played the most important role in the deposition progress in the PS and the HTS.In addition,although the condensation of KCl in the LTSs also happened,the deposition of ash particles played a more important role.
文摘In this paper we consider the relaxation limits of the two-fluid Euler-Maxwellsystems with initial layer. We construct an asymptotic expansion with initial layerfunctions and prove the convergence between the exact solutions and the approximatesolutions.
