CAJ | 학술논문

KdV-Burgers方程出现在许多物理模型中，是非线性科学领域中的重要模型之一。本文讨论一类具有阻尼和非齐次项的KdV-Burgers方程的概周期解存在性问题。首先利用Galerkin方法构造出方程的有界解，并利用一些数学不等式给出这个解的先验估计；然后利用所得的先验估计和标准的紧致性方法证明方程广义解的存在性；最后证明当方程的非齐次项函数是关于时间变量的概周期函数时，该广义解就是方程的概周期解。
KdV-Burgers방정출현재허다물리모형중，시비선성과학영역중적중요모형지일。본문토론일류구유조니화비제차항적KdV-Burgers방정적개주기해존재성문제。수선이용Galerkin방법구조출방정적유계해，병이용일사수학불등식급출저개해적선험고계；연후이용소득적선험고계화표준적긴치성방법증명방정엄의해적존재성；최후증명당방정적비제차항함수시관우시간변량적개주기함수시，해엄의해취시방정적개주기해。
The KdV-Burgers equation appears in many physical models. It is one of the most important models in nonlinear science. This paper mainly investigates the existence of the almost periodic solution to a class of KdV-Burgers equations with damping and non-homogeneous terms. The bounded solution to this equation is constructed by using the Galerkin method and the priori estimates are given by employing some mathematical inequalities. Then the existence of the generalized solution is proved by means of the obtained priori estimates and the standard compact method. Finally, it is proved that the generalized solution is the almost periodic solution to the discussed equation when the non-homogeneous term is an almost periodic function with respect to the time variable.