摘要
主要研究在Dirichlet边界条件或Neumann边界条件下的一类非局部非线性的扩散方程问题.在适当的假设下,证明解的存在性、唯一性、比较原则、以及解对初边值条件的连续依赖性,并就给定的初边值条件,证明解在有限时刻全局爆破.
In this paper, we mainly study a nonlocal nonlinear diffusion equation with Dirichlet boundary conditions or Neumann boundary conditions. Under suitable hypotheses, we will prove existence, uniqueness and the validity of a comparison principle for solutions of these problems, as well as solutions of the problems depend continuously on initial and boundary data. Moreover we will prove that the solution globally blows up in finite time with a given initial and boundary datum.
出处
《纯粹数学与应用数学》
2015年第6期588-595,共8页
Pure and Applied Mathematics
基金
国家自然科学基金(11301419)
四川省教育厅重点项目(13ZA0010
14ZB0143)
西华师范大学大学生科技创新项目(42714081)