Asymptotic behaviour of solutions to semilinear wave equations with initial data of slow decay

✍ Scribed by Hideo Kubo

• Publisher: John Wiley and Sons
• Year: 1994
• Tongue: English
• Weight: 729 KB
• Volume: 17
• Category: Article
• ISSN: 0170-4214
• DOI: 10.1002/mma.1670171205

✦ Synopsis

Abstract

Some useful and remarkable property are derived from a representation formula of a radially symmetric solution to the Cauchy problem for a homogeneous wave equation in odd space dimensions. These properties provide us with enough information to consider the semilinear case, namely, the associated integral equation with the problem will be considered on a weighted L∞‐space. This formulation enables us to deal with the problem for slowly decaying initial data.