This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual ...This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.展开更多
Mn distribution and austenite morphology at the early stage of intercritical annealing of 5Mn steel were investigated. It was experimentally demonstrated that a newly formed 20 nm-thick austenite was formed without th...Mn distribution and austenite morphology at the early stage of intercritical annealing of 5Mn steel were investigated. It was experimentally demonstrated that a newly formed 20 nm-thick austenite was formed without the partitioning of Mn. The elemental analysis confirmed that the growth of austenite should be controlled by the diffusion of C prior to the diffusion of Mn at a low heating rate. The austenite growth started under negligible-partitioning local equilibrium mode and then switched to partitioning local equilibrium mode. Mn segregation at the γ/α interface suggested that the collector plate mechanism was the essential way of Mn partitioning at the early stage of austenite growth.展开更多
基金Project supported by the Fundamental Research Funds for the Central Universities (No. 2009B27514)the National Natural Science Foundation of China (No. 10871059)
文摘This paper is devoted to the analysis of the Cauchy problem for a system of PDEs arising in radiative hydrodynamics. This system, which comes from the so-called equilibrium diffusion regime, is a variant of the usual Euler equations, where the energy and pressure functionals are modified to take into account the effect of radiation and the energy balance containing a nonlinear diffusion term acting on the temperature. The problem is studied in the multi-dimensional framework. The authors identify the existence of a strictly convex entropy and a stability property of the system, and check that the Kawashima-Shizuta condition holds. Then, based on these structure properties, the wellposedness close to a constant state can be proved by using fine energy estimates. The asymptotic decay of the solutions are also investigated.
基金Item Sponsored by National Basic Research Program of China(2010CB630800,2015CB921700)National Natural Science Foundation of China(51001064,51471096)+1 种基金Specialized Research Fund for the Doctoral Program of Higher Education of China(20100002120047)Tsinghua University Initiative Scientific Research Program(20141081200)
文摘Mn distribution and austenite morphology at the early stage of intercritical annealing of 5Mn steel were investigated. It was experimentally demonstrated that a newly formed 20 nm-thick austenite was formed without the partitioning of Mn. The elemental analysis confirmed that the growth of austenite should be controlled by the diffusion of C prior to the diffusion of Mn at a low heating rate. The austenite growth started under negligible-partitioning local equilibrium mode and then switched to partitioning local equilibrium mode. Mn segregation at the γ/α interface suggested that the collector plate mechanism was the essential way of Mn partitioning at the early stage of austenite growth.
