Global Solutions and Interactions of Non-selfsimilar Elementary Waves for n-D Non-homogeneous Burgers Equation  

作　　者：Yuan-an ZHAO Gao-wei CAO Xiao-zhou YANG 

机构地区：[1]University of Chinese Academy of Sciences,Beijing 100049,China [2]School of Mathematics and Statistics,Hubei Minzu University,Enshi 445000,China [3]Wuhan Institute of Physics and Mathematics,Innovation Academy for Precision Measurement Science and Technology,Chinese Academy of Sciences,Wuhan 430071,China

出　　处：《Acta Mathematicae Applicatae Sinica》2023年第4期830-853,共24页应用数学学报（英文版）

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)。

摘　　要：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.

关 键 词：non-homogeneous burgers equation n-dimensional Riemann problem global singular structure non-selfsimilar solution interactions of elementary waves 

分 类 号：O175[理学—数学]