报告人：尹景学（华南师范大学）

时 间：2026年10月20日10:00

地 点：海韵园行政楼C610

内容摘要:

This talk concerns BV solutions of the one-dimensional Cauchy problem for a class of flux-saturated diffusion equations, where the flux saturates at large gradients, the initial data are discontinuous, and the source term may contain singularities. In contrast to most existing studies, which typically exhibit vertical solution profiles at points of discontinuity or restrict the propagation of the jump set to vertical lines, attention is given here to genuinely non-vertical jump discontinuity sets. By exploiting the structural properties of BV functions, the non-monotone flux can be consistently interpreted, and the problem is reformulated as a free-boundary problem governed by an entropy condition. Within this framework, explicit entropy solutions in BV are constructed that originate from discontinuous data, remain discontinuous throughout their evolution, and propagate a jump discontinuity along the curve, while preserving local classical regularity away from the interface. These solutions satisfy a Kruzhkov-type entropy condition but are not necessarily unique for the same initial data. Uniqueness of BV solutions is further established under the additional requirement that the derivative of the flux does not change sign on the jump set. The analysis yields a detailed characterization of the discontinuity dynamics and indicates how hyperbolic features may emerge in flux-saturated diffusion.

个人简介：

尹景学，华南师范大学教授、博导，长江学者奖励计划特聘教授，国家杰出青年基金获得者，国家级教学名师，国务院政府特殊津贴专家。 曾获香港求是科技基金会“杰出青年学者奖”，教育部科学技术进步一等奖（排名第二），教育部高等学校自然科学二等奖（排名第一），教育部高等学校优秀骨干教师，教育部跨世纪优秀人才称号等；主持国家杰出青年基金项目、重点项目、面上项目，霍英东青年教师基金项目，高等学校博士学科点专项科研基金项目，教育部基地创名牌课程项目，国家精品课项目等多项科研和教学项目；出版专著教材7部；在国内外高水平学术刊物上发表论文100余篇。

联系人：王焰金