论文标题
Shigesada-Kawasaki-teramoto交叉扩散系统超出了详细的平衡
The Shigesada-Kawasaki-Teramoto cross-diffusion system beyond detailed balance
论文作者
论文摘要
事实证明，全球薄弱的解决方案的存在证明了shigesada，川崎和Teramoto的交叉扩散模型。该模型由具有无升华边界条件的有界域中的人口密度强耦合抛物线方程组成，它描述了种群种群种族隔离的动力学。扩散矩阵既不是对称的，也不是阳性半芬矿。一个新的对数熵允许对严重非对称扩散矩阵的系数改善条件，而不会施加文献中经常假设的详细平衡条件。此外，通过使用与对数熵相关的相对熵证明，溶液向恒定稳态的较大时间收敛。
The existence of global weak solutions to the cross-diffusion model of Shigesada, Kawasaki, and Teramoto for an arbitrary number of species is proved. The model consists of strongly coupled parabolic equations for the population densities in a bounded domain with no-flux boundary conditions, and it describes the dynamics of the segregation of the population species. The diffusion matrix is neither symmetric nor positive semidefinite. A new logarithmic entropy allows for an improved condition on the coefficients of heavily nonsymmetric diffusion matrices, without imposing the detailed-balance condition that is often assumed in the literature. Furthermore, the large-time convergence of the solutions to the constant steady state is proved by using the relative entropy associated to the logarithmic entropy.
