Mild solutions to a measure-valued mass evolution problem with flux boundary conditions
Mild solutions to a measure-valued mass evolution problem with flux boundary conditions
复制标题
DOI：
10.1016/j.jde.2015.02.037
复制
发表时间：
2015-08-05
影响因子：
2.4
通讯作者：
Muntean, Adrian
中科院分区：
文献类型：
--
作者：
Evers, Joep H. M.;Hille, Sander C.;Muntean, Adrian
研究了一类在有限Borel测度空间M（[0,1]）上具有线性不连续产生项的单位区间[0,1]上线性输运方程温和解的适定性和逼近性。我们的工作技术包括详细的边界层分析，根据半群表示的解决方案的空间措施能够处理通道到奇异极限，其中层的厚度消失。我们不仅得到了所选测度值演化问题解的合适概念，而且推导出了逼近过程的收敛速率，并对极限问题的通量边界条件的结构有了深入的了解。(C) 2015爱思唯尔公司版权所有。
We investigate the well-posedness and approximation of mild solutions to a class of linear transport equations on the unit interval [0, 1] endowed with a linear discontinuous production term, formulated in the space M([0, 1]) of finite Borel measures. Our working technique includes a detailed boundary layer analysis in terms of a semigroup representation of solutions in spaces of measures able to cope with the passage to the singular limit where thickness of the layer vanishes. We obtain not only a suitable concept of solutions to the chosen measure-valued evolution problem, but also derive convergence rates for the approximation procedure and get insight in the structure of flux boundary conditions for the limit problem. (C) 2015 Elsevier Inc. All rights reserved.