报告题目：Existence of Asymmetric Grain Boundaries
时 间：2026年07月24日(星期五) 10：00
地 点：科研楼18号楼1102
主 办：数学与统计学院、分析数学及应用教育部重点实验室、福建省分析数学及应用重点实验室、统计学与人工智能福建省高校重点实验室、福建省应用数学中心（福建师范大学）
参加对象：感兴趣的老师和研究生
报告摘要：Grain boundaries, as interfaces separating distinct orientations of spatially periodic patterns, are among the most ubiquitous defect structures in nature, and play a fundamental role in pattern selection, defect dynamics, and material properties. In this work, we establish the existence of asymmetric grain boundaries in the Swift-Hohenberg equation, substantially extending earlier results restricted to symmetric configurations. The analysis presents two major challenges: first, establishing the existence of the relevant heteroclinic orbit in the leading-order cubic normal form through a delicate variational argument; and second, proving its persistence in the full reduced system via delicate spectral analysis, a refined Lyapunov-Schmidt reduction, and the explicit computation of a quintic normal form.
报告人简介：吴启亮，俄亥俄大学教授，博士生导师，主要研究方向为非线性动力学和模式形成。在J. Math. Pures Appl.，Proc. Amer. Math. Soc.，J. Differential Eqns.，J. Math. Biol.，J. Dyn. Diff. Eqns.，Discrete Contin. Dyn. Syst.等刊物上发表多篇论文。曾获美国国家自然科学基金资助。