# American Institute of Mathematical Sciences

March  2011, 1(1): 61-81. doi: 10.3934/mcrf.2011.1.61

## Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain

 1 Department of Mathematical Sciences, University of Cincinnati, Cincinnati, Oh 45221, United States, United States 2 Department of Mathematics, University of Dayton, Dayton, OH 45431, United States

Received  October 2010 Revised  January 2011 Published  March 2011

In this paper, we study a class of initial boundary value problem (IBVP) of the Korteweg-de Vries equation posed on a finite interval with nonhomogeneous boundary conditions. The IBVP is known to be locally well-posed, but its global $L^2$- a priori estimate is not available and therefore it is not clear whether its solutions exist globally or blow up in finite time. It is shown in this paper that the solutions exist globally as long as their initial value and the associated boundary data are small, and moreover, those solutions decay exponentially if their boundary data decay exponentially.
Citation: Ivonne Rivas, Muhammad Usman, Bing-Yu Zhang. Global well-posedness and asymptotic behavior of a class of initial-boundary-value problem of the Korteweg-De Vries equation on a finite domain. Mathematical Control & Related Fields, 2011, 1 (1) : 61-81. doi: 10.3934/mcrf.2011.1.61
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