由Dirichlet到Neumann映射重构平面上椭圆型方程对流系数的一种方法
被引量：2
摘要
讨论了由Dirichlet到Neumann映射重构平面上二阶椭圆型方程的对流系数的问题.这是一个高度非线性和不适定的问题.利用广义解析函数理论和关于一阶椭圆型方程组的逆散射方法的技巧,给出了一种构造性方法.
出处
《中国科学（A辑）》
CSCD
北大核心
2004年第6期752-766,共15页
Science in China(Series A)
基金
国家自然科学基金(批准号:10271032)上海市教委曙光计划E-研究院基金资助项目
参考文献17
-
1Kohn R, Vogelius M. Determining conductivity by boundary measurements. Comm Pure Appl Math,1984, 37:289-298
-
2Kohn R, Vogelius M. Determining conductivity by boundary measurements, Ⅱ. Interior Results Comm Pure Appl Math, 1985, 38:643-667
-
3Sylvester J, Uhlmann G. A global uniqueness theorem for an inverse boundary value problem. Ann of Math, 1987, 125:153-169
-
4Nachman A I. Reconstructions from boundary measurements. Ann of Math, 1988, 128:531-576
-
5Nachman A I. Global uniqueness for a two-dimensional inverse boundary value problem. Ann of Math,1995, 142:71-96
-
6Barcelo J A, Barcelo T, Ruiz A. Stability of the inverse conductivity problem in the plane for less regular conductivities. J of Differential Equations, 2001, 173: 231 -270
-
7Brown R M, Uhlmann G. Uniqueness in the inverse conductivity problem for nonsmooth conductives in two dimensions. Commun in Partial Differential Equations, 1997, 22:1009-1027
-
8Isakov V. Inverse Problems for Partial Differential Equations. New York: Springer-Verlag, 1998
-
9Cheng J, Nakamura G, Somersalo E. Uniqueness of identifying the convection term. Comm Korean Math Soc, 2001, 16:405-413
-
10Nakamura G, Sun Z, Uhlmann G. Global identifiability for an inverse problem for the Schrodinger equation in a magnetic field. Math Ann, 1995, 303:377-388
同被引文献39
-
1刘继军,程晋,中村玄.Reconstruction and uniqueness of an inverse scattering problem with impedance boundary[J].Science China Mathematics,2002,45(11):1408-1419. 被引量：7
-
2CHEN WenBin,CHENG Jin,LIN JunShan,WANG LiFeng.A level set method to reconstruct the discontinuity of the conductivity in EIT[J].Science China Mathematics,2009,52(1):29-44. 被引量：6
-
3WANG HaiBing 1,2 & LIU JiJun 1 1 Department of Mathematics,Southeast University,Nanjing 210096,China,2 School of Mathematics and Computational Science,Hunan University of Science and Technology,Xiangtan 411201,China.On the reconstruction of Dirichlet-to-Neumann map in inverse scattering problems with stability estimates[J].Science China Mathematics,2010,53(8):2069-2084. 被引量：2
-
4冯立新,马富明.洞穴逆散射问题解的惟一性与局部稳定性[J].中国科学（A辑）,2005,35(6):641-650. 被引量：1
-
5Kohn R V, Vogelius M. Determining conductivity by boundary measurements. Commun Pure Appl Math, 37:113-123 (1984)
-
6Liu J J, Cheng J, Nakamura G. Reconstruction and uniqueness of an inverse scattering problem with impedance boundary. Sci China Set A-Math, 45(11): 1408 -1419 (2002)
-
7Osher S, Sethian JA. Fronts propagating with curvature-dependent speed: algorithms based on Hamilton- Jacobi formulations. J Comput Phys, 79:12-49 (1988)
-
8Osher S, Fedkiw R. Level set methods and Dynamic Implicit surfaces. In: Applied Mathematical Sciences, Vol 153. New York: Springer, 2003
-
9Santosa F. A level set approach for inverse problems involving obstacles. ESAIM, Control Optim Calculus Variations, 1:17- 33 (1996)
-
10Dorn O, Lesselier D. Lever set method for inverse scattering. Inverse Problems, 22:67-131 (2006)
引证文献2
-
1林俊杉,陈文斌,程晋,王立峰.重构电导率间断界面的一种水平集方法[J].中国科学（A辑）,2009,39(2):233-246.
-
2陈贞华,陈文斌,程晋,刘源.一类带Stenfen-Boltzmann边界条件的热输运反问题的单调算法[J].中国科学：数学,2012,42(5):361-376. 被引量：1
-
1刘慕仁,何云,陈若航,孔令江.一维对流扩散方程的格子Boltzmann方法[J].广西科学,1999,6(3):168-169. 被引量：2
-
2赵凯宏.半线性椭圆型偏微分方程反问题解的整体惟一性[J].玉溪师范学院学报,2006,22(9):65-72.
-
3董积旖,宗培.高雷诺数射流冲击对流系数的计算及数值分析[J].冶金能源,2012,31(4):26-29. 被引量：1
-
4邓敏艺,刘慕仁,孔令江.二维对流扩散方程的格子Boltzmann方法模拟[J].广西师范大学学报（自然科学版）,1999,17(3):1-5. 被引量：5
-
5丁俊堂.一类一阶椭圆型方程组的最大值原理[J].山西大学学报（自然科学版）,1991,14(4):339-344.
-
6李珏,李华兵,孔令江,刘慕仁.Burgers方程定态激波解的格子Boltzmann方法模拟[J].广西师范大学学报（自然科学版）,2000,18(2):1-5. 被引量：3
-
7陈向阳,蓝师义.半圆域内的二维线性椭圆偏微分方程（英文）[J].数学杂志,2015,35(5):1148-1158.
-
8冯立新,贾念念.利用观测数据确定传导方程系数的稳定性[J].哈尔滨工业大学学报,2009,41(12):213-215.
-
9李静,胡真.基于Dirichlet-to-Neumann映射计算二维蜂巢状光子晶体的带隙结构[J].江南大学学报（自然科学版）,2015,14(6):875-881. 被引量：1
-
10童重亮.一类平面非线性椭圆型方程反问题的唯一性[J].复旦学报（自然科学版）,2005,44(2):280-286.
