论文摘要
本文研究单个非线性双曲守恒律的n维Riemann初边值问题,其中边界为n-1维光滑流形,初值和边界值各为常数。以二维情形为代表,研究了边界条件的表达式和几何特征,给出了单个守恒律的二维一般初边值问题的分片光滑弱熵解满足的条件,包括Rankine-Hugoniot边界面条件、内部熵条件不等式、边界熵条件不等式等。根据唯一性,构造性的给出了单个守恒律的二维Riemann初边值问题的整体弱熵解。首先构造了对应的单个守恒律的二维Riemann初值问题的整体弱熵解,验证它满足Rankine-Hugoniot间断面条件、内部熵条件不等式等,将所得解限制在边界范围内,再验证它满足边界熵条件不等式,从而得到单个守恒律的二维Riemann初边值问题的非自模型的整体弱熵解。并分别在弯曲边界和直线边界的情形给出了两个实例,推导了解的表达式,进行了数值仿真。最后将所建立的方法推广到n维情形。
论文目录
相关论文文献
- [1].Mapping of Least ρ-Dirichlet Energy between Doubly Connected Riemann Surfaces[J]. Acta Mathematica Sinica 2020(06)
- [2].The Riemann Problem for Chaplygin Gas Flow in a Duct with Discontinuous Cross-Section[J]. Chinese Annals of Mathematics,Series B 2020(04)
- [3].Riemann函数性质及实数完备性的推导[J]. 科技经济市场 2019(07)
- [4].Riemann–Hilbert-type Boundary Value Problems on a Half Hexagon[J]. Acta Mathematica Sinica 2017(09)
- [5].Generalized Riemann problem for Euler system Dedicated to Professor LI TaTsien on the Occasion of His 80th Birthday[J]. Science China(Mathematics) 2017(04)
- [6].Inverse Scattering Transform of the Coupled Sasa–Satsuma Equation by Riemann–Hilbert Approach[J]. Communications in Theoretical Physics 2017(05)
- [7].非齐次非对称Keyfitz-Kranzer气体方程组的Riemann问题[J]. 四川师范大学学报(自然科学版) 2020(06)
- [8].Multi-Soliton Solutions for the Coupled Fokas–Lenells System via Riemann–Hilbert Approach[J]. Chinese Physics Letters 2018(07)
- [9].Perturbed Riemann Problem for a Scalar Chapman-Jouguet Combustion Model[J]. Chinese Annals of Mathematics(Series B) 2015(02)
- [10].Automorphism Groups of Pseudo-real Riemann Surfaces of Low Genus[J]. Acta Mathematica Sinica 2014(01)
- [11].Riemann映射与单连通区域分类[J]. 中国科学:数学 2013(03)
- [12].Riemann boundary value problems and reflection of shock for the Chaplygin gas[J]. Science China(Mathematics) 2012(04)
- [13].THE VANISHING PRESSURE LIMIT OF SOLUTIONS TO THE SIMPLIFIED EULER EQUATIONS FOR ISENTROPIC FLUIDS[J]. Annals of Differential Equations 2012(01)
- [14].Riemann-Stieltjes可积的充要条件[J]. 北京师范大学学报(自然科学版) 2011(02)
- [15].ON MNTS FORMULA[J]. Acta Mathematica Scientia 2010(01)
- [16].Two-Dimensional Riemann Problems for the Compressible Euler System[J]. Chinese Annals of Mathematics 2009(06)
- [17].广义解析函数的广义Riemann-Hilbert问题[J]. 华东理工大学学报(自然科学版) 2009(06)
- [18].Global Structure Stability of Riemann Solution of Quasilinear Hyperbolic System of Conservation Law in Presence of Boundary:Shocks and Contact Discontinuities[J]. Communications in Theoretical Physics 2008(11)
- [19].An application of the Riemann-Roch theorem[J]. Science in China(Series A:Mathematics) 2008(04)
- [20].Multiple Positive Solutions to Singular Fractional Differential System with Riemann-Stieltjes Integral Boundary Condition[J]. Communications in Mathematical Research 2019(03)
- [21].关于向量值函数Riemann积分的若干研究[J]. 云南大学学报(自然科学版) 2019(05)
- [22].A Riemann-Hilbert Approach to the Chen-Lee-Liu Equation on the Half Line[J]. Acta Mathematicae Applicatae Sinica 2018(03)
- [23].A Riemann-Hilbert Approach to the Harry-Dym Equation on the Line[J]. Chinese Annals of Mathematics(Series B) 2016(03)
- [24].二维实系数线性双曲型方程组角域上的Riemann问题（英文）[J]. 应用数学与计算数学学报 2015(03)
- [25].Riemann-Hilbert Problem and Its Well-Posed-Ness for Elliptic Complex Equations of First Order in Multiply Connected Domains[J]. Journal of Mathematical Research with Applications 2014(04)
- [26].关于Riemann可积理论的教学探讨[J]. 高等数学研究 2012(06)
- [27].半平面中一类Riemann-Hilbert边值逆问题[J]. 贵州师范大学学报(自然科学版) 2011(01)
- [28].Riemann-Stieltjes可积函数的本质[J]. 西华大学学报(自然科学版) 2009(06)
- [29].保角变换法解无穷曲线上的Riemann边值问题[J]. 宁夏师范学院学报 2009(06)
- [30].Remarks on Thurston's Construction of Pseudo-Anosov Maps of Riemann Surfaces[J]. Chinese Annals of Mathematics 2008(01)