We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu...We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.展开更多
We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small per...We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption θ_i,+/θ_e,+=θ_i,-/θ_e,-≥m_i/2m_e,namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile,we obtain the global existence of solutions based on energy method.展开更多
We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the exi...We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed.展开更多
基金The research was supported by the National Natural Science Foundation of China #10625105 and #10431060, the Program for New Century Excellent Talents in University #NCET-04-0745. Acknowledgement Authors would like to thank the anonymous referee for his/her helpful suggestions and comments.
文摘We consider the asymptotic behavior of solutions to a model of hyperbolicelliptic coupled system on the half-line R＋ = （0, ∞）,with the Dirichlet boundary condition u（0, t） = 0. S. Kawashima and Y. Tanaka [Kyushu J. Math., 58（2004）, 211-250] have shown that the solution to the corresponding Cauchy problem behaviors like rarefaction waves and obtained its convergence rate when u_ u＋. Our main concern in this paper is the boundary effect. In the case of null-Dirichlet boundary condition on u, asymptotic behavior of the solution （u, q） is proved to be rarefaction wave as t tends to infinity. Its convergence rate is also obtained by the standard L2-energy method and Ll-estimate. It decays much lower than that of the corresponding Cauchy problem.
基金supported by the General Research Fund from Research Grants Council of Hong Kong(Grant No.400912)National Natural Science Foundation of China(Grant Nos.11101188+1 种基金11471142and 11331005)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT13066)
文摘We study the large-time asymptotics of solutions toward the weak rarefaction wave of the quasineutral Euler system for a two-fluid plasma model in the presence of diffusions of velocity and temperature under small perturbations of initial data and also under an extra assumption θ_i,+/θ_e,+=θ_i,-/θ_e,-≥m_i/2m_e,namely, the ratio of the thermal speeds of ions and electrons at both far fields is not less than one half. Meanwhile,we obtain the global existence of solutions based on energy method.
基金supported by National Natural Science Foundation of China(Grant No.11331005)the Program for Changjiang Scholars and Innovative Research Team in University(Grant No.IRT13066)+1 种基金the Special Fund for Basic Scientific Research of Central Colleges(Grant No.CCNU12C01001)Excellent Doctorial Dissertation Cultivation Grant from Central Normal University
文摘We study the initial boundary value problem to the system of the compressible Navier-Stokes equations coupled with the Maxwell equations through the Lorentz force in a bounded annulus Ω of R3. And a result on the existence and uniqueness of global spherically symmetric classical solutions is obtained. Here the initial data could be large and initial vacuum is allowed.
