Lp estimates of solutions of some partial differential equations

✍ Scribed by Linghai Zhang

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 184 KB
• Volume: 56
• Category: Article
• ISSN: 0362-546X
• DOI: 10.1016/j.na.2003.09.005

✦ Synopsis

The author is concerned with the long time asymptotic behaviors of the global weak solutions of some nonlinear evolution equations. First of all, he derives some uniform L 1 and L ∞ upper bounds for the solutions, under some mild conditions. Then, by applying the well-known Fourier splitting method and the L 1 estimates, he asserts the L 2 decay estimates of the solutions. The rates of decay are sharp in the sense that the integral of the initial data over R is nonzero.