EXISTENCE THEORY OF THE INITIAL VALUE PROBLEM FOR THE KdVB EQUATION
碩士 === 國立高雄師範大學 === 數學系 === 90 === In this paper, we study the existence, uniqueness and regularity dependence results which are established for the initial value problem to the KdVB equation, $$u_t+uu_x-\alpha u_{xx}+u_{xxx}=0.$$ The methods used in this paper is t...
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| Format: | Others |
| Language: | en_US |
| Published: |
2002
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| Online Access: | http://ndltd.ncl.edu.tw/handle/98235615628866357126 |
| Summary: | 碩士 === 國立高雄師範大學 === 數學系 === 90 === In this paper, we study the existence, uniqueness and regularity dependence results which are established for the initial value problem to the KdVB equation,
$$u_t+uu_x-\alpha u_{xx}+u_{xxx}=0.$$
The methods used in this paper is to regularize the KdVB equation by the addition of the linear term $-\epsilon u_{xxt},$ hence the existence and uniqueness theory for the initial value problem will be developed by the BBMB equation. Finally we consider the limit $\epsilon \to 0$ to show the strong convergence to solutions of the initial value problem for the KdVB equation.
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