标题： 非局部到局部的$p$-双调和演化方程在狄利克雷边界条件下的收敛性 显示英文标题

标题： Nonlocal-to-local convergence of the $p$-Biharmonic evolution equation with the Dirichlet boundary condition

摘要： 本文研究了在图像处理和数据分析中出现的带有狄利克雷边界条件的非局部$p$-双调和演化方程。我们证明了非局部方程解的存在性和唯一性，并讨论了解的大时间行为。通过适当缩放非局部核，我们进一步表明解收敛到带有狄利克雷边界条件的经典$p$-双调和方程的解。 显示英文摘要

摘要： This paper studies the nonlocal $p$-biharmonic evolution equation with the Dirichlet boundary condition that arises in image processing and data analysis. We prove the existence and uniqueness of solutions to the nonlocal equation and discuss the large time behavior of the solution. By appropriately rescaling the nonlocal kernel, we further show that the solution converges to the solution of the classical $p$-biharmonic equation with the Dirichlet boundary condition.