IJPAM: Volume 34, No. 2 (2007)

ON THE WELL-POSEDNESS PROBLEM FOR
THE GENERALIZED b-FAMILY OF EQUATIONS

Peng Dejun$^1$, Zhang Chengyi$^2$
$^{1,2}$Department of Mathematics
Hainan Normal University
Hainan, Haikou, 571158, P.R. CHINA


Abstract.In this paper, we study the local well posedness of the Cauchy problem for the generalized b-family equations. By applying some Sobolev's inequalities, semigroup theorem and related knowledge of PDE and using Kato's theory, we prove that there is a unique local solution of this problem which is continuously depending on the initial value.

Received: October 31, 2006

AMS Subject Classification: 35F10

Key Words and Phrases: b-family of equations, Kato's theory, local well posedness

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 2