高维BBM-Burgers方程解的存在性

Existence of Solutions of Multi-dimensional BBM-Burgers Equation

研究了高维空间Benjamin-Bona-Mahony-Burgers方程在大初值情况下解的整体存在性.首先通过构造一个完备度量空间的柯西序列,得到解的局部存在性,然后借助格林函数,能量估计等工具得到解的整体有界性估计,由逐步递推的办法,最后得到解的整体存在性.

In the report,the global existence of solution to Benjamin-Bona-Mahony-Burgers equation with large initial data in multi space dimension was investigated. A Cauchy sequence in a Banach space was constructed,and the local existence of solution was obtained. Green function and energy estimate etc,were used to obtain the global bounded estimate of the solution. Then,the global existence of solution was obtained step by step.