Asymptotic Stability of Planar Rarefaction Waves for the Relaxation Approximation of Conservation Laws in Several Dimensions

✍ Scribed by Tao Luo

• Publisher: Elsevier Science
• Year: 1997
• Tongue: English
• Weight: 539 KB
• Volume: 133
• Category: Article
• ISSN: 0022-0396
• DOI: 10.1006/jdeq.1996.3214

✦ Synopsis

This paper concerns the large time behavior toward planar rarefaction waves of solutions for the relaxation approximation of conservation laws in several dimensions. It is shown that a planar rarefaction wave is nonlinear stable in the sense that it is an asymptotic attractor for the relaxation approximation of conservation laws.

1997 Academic Press

where A i =a i I, a i >0, i=1, 2, ..., m, and I is an n_n unit matrix. A numerical scheme to solve (1.2), (1.3) was designed in [8]. The main features of this scheme are its generality and simplicity.