论文标题
一类退化交叉扩散系统的弱解决方案有限
Bounded Weak Solutions to a Class of Degenerate Cross-Diffusion Systems
论文作者
论文摘要
有界弱的溶液是为具有完整扩散矩阵的退化抛物线系统构建的，该系统是薄膜Muskat系统的广义版本。借助序列$（\ Mathcal {e} _n）_ {n \ ge 2} $的liapunov功能，以实现有限性，以至于$ n \ n \ ge 2 $ and $ n \ ge 2 $ and $ n $ norm等于$ \ mathcal {e} _n $ nom $ l_ \ infty $ -norm在限制$ n \ to \ infty $中。薄弱的解决方案是通过紧凑的方法建造的，在建造近似过程中需要特殊护理，以保留上述Liapunov功能的可用性。
Bounded weak solutions are constructed for a degenerate parabolic system with a full diffusion matrix, which is a generalized version of the thin film Muskat system. Boundedness is achieved with the help of a sequence $(\mathcal{E}_n)_{n\ge 2}$ of Liapunov functionals such that $\mathcal{E}_n$ is equivalent to the $L_n$-norm for each $n \ge 2$ and $\mathcal{E}_n^{1/n}$ controls the $L_\infty$-norm in the limit $n\to\infty$. Weak solutions are built by a compactness approach, special care being needed in the construction of the approximation in order to preserve the availability of the above-mentioned Liapunov functionals.
