中文摘要：

研究在非线性边界流条件下,薄膜方程一类非负弱解的存在性,其定义采取分部积分两次来给出.通过构造合适的逼近方程来克服非线性边界流的影响.为获得与逼近参数无关的一致能量估计,需利用熵泛函方法.最后,以紧性定理为基础,获得小参数趋于零的极限,进而证得弱解存在性.

英文摘要：

The existence of a class of nonegative weak solutions with a nonlinear boundary flux is studied,and the definition is given by applying partial integration twice.By constructing a reasonable approximation problem,the effect of nonlinear boundary is overcomed.In order to obtain the uniform estimates independent of the approximation parameter,the entropy needs to be applied.Finally,the limit of small parameter is gained by compactness theorem,and then the existence is proved.