The Stability of the Linear Transport Equation in a Nonmultiplying Medium

✍ Scribed by Xianwen Zhang

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 116 KB
• Volume: 262
• Category: Article
• ISSN: 0022-247X
• DOI: 10.1006/jmaa.2001.7562

✦ Synopsis

The stability of the linear transport equation is established when the host medium is nonmultiplying and occupies a bounded convex body. Under the assumption that the minimal value of the collision frequency or the minimal speed of the transport particles is larger than zero, the exponential stability is proven. When this condition is not valid, the stability (but nonexponential stability) result is obtained.  2001 Academic Press Here x ∈ D, D ⊂ R 3 is a bounded convex and open set where transport process takes place, and ξ

where V is the velocity domain of the particles involved in the transport processes. Throughout the paper, we assume the following:

1. The collision frequency h x ξ and the energy transport kernel k x ξ ξ are bounded nonnegative and measurable functions defined in D × V and D × V × V , respectively.