In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. Th...In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of twodimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u＋ 〉 0, while explicit non-selfsirnilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u＋ 〈 0. The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.展开更多
We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-...We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.展开更多
We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt w...We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt with, even for complex interaction of combustion waves. Furthermore, we analyze the way in which the area of unburnt gas shrinks.展开更多
我们为 n 调查单个结构维的 non-selfsimilarglobal 解决方案和 non-selfsimilar 的相互作用 n 的基本波浪维的 Burgersequation 在起始的断绝是 n 的地方，维的光滑的表面和起始的数据就包含二个不同经常的状态，全球解决方案和一些新...我们为 n 调查单个结构维的 non-selfsimilarglobal 解决方案和 non-selfsimilar 的相互作用 n 的基本波浪维的 Burgersequation 在起始的断绝是 n 的地方，维的光滑的表面和起始的数据就包含二个不同经常的状态，全球解决方案和一些新现象被发现。Anelegant 技术被建议构造 n 没有维的减小或并列转变的维的冲击波。展开更多
For the two-dimensional(2D)scalar conservation law,when the initial data contain two different constant states and the initial discontinuous curve is a general curve,then complex structures of wave interactions will b...For the two-dimensional(2D)scalar conservation law,when the initial data contain two different constant states and the initial discontinuous curve is a general curve,then complex structures of wave interactions will be generated.In this paper,by proposing and investigating the plus envelope,the minus envelope,and the mixed envelope of 2D non-selfsimilar rarefaction wave surfaces,we obtain and the prove the new structures and classifications of interactions between the 2D non-selfsimilar shock wave and the rarefaction wave.For the cases of the plus envelope and the minus envelope,we get and prove the necessary and sufficient criterion to judge these two envelopes and correspondingly get more general new structures of 2D solutions.展开更多
Two-dimensional Riemann problem for scalar conservation law are investigated and classification of global structure for its nomselfsimilar solution is given by analysis of structure and classification of envelope for ...Two-dimensional Riemann problem for scalar conservation law are investigated and classification of global structure for its nomselfsimilar solution is given by analysis of structure and classification of envelope for non-selfsimilar 2D rarefaction wave. Initial data has two different constant states which are separated by initial discontinuity. We propose the concepts of plus envelope, minus envelope and mixed envelope, and some new structures and evolution phenomena are discovered by use of these concepts.展开更多
基金Sponsored by the National Natural Science Foundation of China (10671116,10871199, and 10001023)Hou Yingdong Fellowship (81004), The China Scholarship Council, Scientific Research Foundation for the Returned Overseas Chinese Scholars, State Education Ministry, Natural Science Foundation of Guangdong (06027210 and 000804)Natural Science Foundation of Guangdong Education Bureau (200030)
文摘In this article, we get non-selfsimilar elementary waves of the conservation laws in another kind of view, which is different from the usual self-similar transformation. The solution has different global structure. This article is divided into three parts. The first part is introduction. In the second part, we discuss non-selfsimilar elementary waves and their interactions of a class of twodimensional conservation laws. In this case, we consider the case that the initial discontinuity is parabola with u＋ 〉 0, while explicit non-selfsirnilar rarefaction wave can be obtained. In the second part, we consider the solution structure of case u＋ 〈 0. The new solution structures are obtained by the interactions between different elementary waves, and will continue to interact with other states. Global solutions would be very different from the situation of one dimension.
基金partly supported by the National Natural Science Foundation of China (Grant11701551 and Grant 11971024)partly supported by the National Natural Science Foundation of China (Grant 11471332)。
文摘We investigate the global structures of the non-selfsimilar solutions for n-dimensional(n-D) nonhomogeneous Burgers equation, in which the initial data has two different constant states, which are separated by a(n-1)-dimensional sphere. We first obtain the expressions of n-D shock waves and rarefaction waves emitting from the initial discontinuity. Then, by estimating the new kind of interactions of the related elementary waves,we obtain the global structures of the non-selfsimilar solutions, in which ingenious techniques are proposed to construct the n-D shock waves. The asymptotic behaviors with geometric structures are also proved.
基金Supported by the National Natural Science Foundation of China(No.10871199 and 11071246)
文摘We investigate the Chapman-Jouguet model in multi-dimensional space, and construct explicitly its non-selfsimilar Riemann solutions. By the method we apply in this paper, general initial discontinuities can be dealt with, even for complex interaction of combustion waves. Furthermore, we analyze the way in which the area of unburnt gas shrinks.
基金Supported by the National Natural Science Foundation （10001023）, Huo Ying-dong Fellowship （81004）, Scientific Research Foundation for the Returned 0verseas Chinese Scholars, State Education Ministry, The China Scholarship Council, Natural Science Foundation of Guangdong （000804） and Natural Science Foundation of Guangdong Education Bureau （200030）
文摘我们为 n 调查单个结构维的 non-selfsimilarglobal 解决方案和 non-selfsimilar 的相互作用 n 的基本波浪维的 Burgersequation 在起始的断绝是 n 的地方，维的光滑的表面和起始的数据就包含二个不同经常的状态，全球解决方案和一些新现象被发现。Anelegant 技术被建议构造 n 没有维的减小或并列转变的维的冲击波。
基金supported in part by the NSFC(Grant No.11471332)The research of Gao-wei Cao was supported in part by the NSFC(Grant No.11701551).
文摘For the two-dimensional(2D)scalar conservation law,when the initial data contain two different constant states and the initial discontinuous curve is a general curve,then complex structures of wave interactions will be generated.In this paper,by proposing and investigating the plus envelope,the minus envelope,and the mixed envelope of 2D non-selfsimilar rarefaction wave surfaces,we obtain and the prove the new structures and classifications of interactions between the 2D non-selfsimilar shock wave and the rarefaction wave.For the cases of the plus envelope and the minus envelope,we get and prove the necessary and sufficient criterion to judge these two envelopes and correspondingly get more general new structures of 2D solutions.
基金supported by National Natural Science Foundation of China(Grant No:11071246,10671116)
文摘Two-dimensional Riemann problem for scalar conservation law are investigated and classification of global structure for its nomselfsimilar solution is given by analysis of structure and classification of envelope for non-selfsimilar 2D rarefaction wave. Initial data has two different constant states which are separated by initial discontinuity. We propose the concepts of plus envelope, minus envelope and mixed envelope, and some new structures and evolution phenomena are discovered by use of these concepts.
