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

• Published in: Acta Mathematicae Applicatae Sinica Vol. 39; no. 4; pp. 830 - 853
• Main Authors: Zhao, Yuan-an, Cao, Gao-wei, Yang, Xiao-zhou
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-10-2023; Springer Nature B.V
• Edition: English series
• Subjects: Applications of Mathematics; Asymptotic properties; Burgers equation; Math Applications in Computer Science; Mathematical and Computational Physics; Mathematics; Mathematics and Statistics; Rarefaction; Shock waves; Theoretical; 35F25; 35F21; global singular structure; 35A02; 35D40; dimensional Riemann problem; non-selfsimilar solution; interactions of elementary waves; 35L67; 35L65; non-homogeneous burgers equation
• ISSN: 0168-9673; 1618-3932
• DOI: 10.1007/s10255-023-1097-9

We investigate the global structures of the non-selfsimilar solutions for
n
-dimensional (
n
-D) non-homogeneous 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.