论文标题
不断发展的域上的散装系统
Bulk-surface systems on evolving domains
论文作者
论文摘要
研究了不断发展的域上的散装面系统。这些问题通常来自生物细胞中的受体 - 配体动力学的建模。我们的第一个主要结果是在所有维度中的全球存在和解决方案的界限。这是通过证明抛物线方程的$ l^p $ - 最大规律性和移动表面上具有二元性方法的定期性，这是独立的。第二个主要结果是我们显示的较大的时间动力学，假设移动域/表面的体积/面积不变，并且材料速度在很大的时间内衰减，则该溶液会收敛到独特的空间均匀平衡。通过将熵方法扩展到不断发展的域中的宽大表面系统来证明结果。
Bulk-surface systems on evolving domains are studied. Such problems appear typically from modelling receptor-ligand dynamics in biological cells. Our first main result is the global existence and boundedness of solutions in all dimensions. This is achieved by proving $L^p$-maximal regularity of parabolic equations and duality methods in moving surfaces, which are of independent interest. The second main result is the large time dynamics where we show, under the assumption that the volume/area of the moving domain/surface is unchanged and that the material velocities are decaying for large time, that the solution converges to a unique spatially homogeneous equilibrium. The result is proved by extending the entropy method to bulk-surface systems in evolving domains.
