Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8899897 | Journal of Mathematical Analysis and Applications | 2018 | 12 Pages |
Abstract
We consider the Lâ weak solutions to a type of compressible Euler equation with dissipation effects. Several studies [6], [14], [30] have obtained the Lâ weak solutions to this type of system by using numerical schemes and the compensated compactness method. Therefore, the uniform boundedness of approximate solutions and the Hlocâ1 compactness of the corresponding entropy dissipation measures must be considered. It should be noted that the obtained Lâ bounds typically increase over time. However, getting a time-independent uniform bound is important to consider the large time behavior of weak solutions. In this paper, by using invariant region theory, we prove that the Lâ weak solutions derived by the Lax-Friedrichs scheme are uniformly bounded in time.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Xixi Fang, Huimin Yu,