-loss of derivatives for an evolution type model

✍ Scribed by Daoyuan Fang; Xiaojun Lu; Michael Reissig

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 761 KB
• Volume: 71
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2009.04.027

✦ Synopsis

This paper is devoted to the study of loss of derivatives for an evolution type model, which allows for non-integer powers of (-∆). On the one hand, we describe the influence from the orders of principle symbols. On the other hand, we explore the significant impact of ν-related oscillation from the pseudo-differential operators. In the final analysis, to demonstrate the sharpness of our estimates, counter-examples are constructed through the application of Floquet theory and instability arguments.