报告题目：On Kirchhoff-type evolution equations involving the fractional Laplacian
报 告 人：张彬林
工作单位：山东科技大学
报告时间：2021-06-24 09:00-10:00
腾讯会议ID： 370 441 489
报告摘要：
In this talk, we first discuss a diffusion model of Kirchhoff-type driven by fractional Laplace operator. Under some appropriate conditions, the local existence of nonnegative solutions is obtained by employing the Galerkin method. Then, by means of a differential inequality technique, we prove that the local nonnegative solutions blow up in finite time with arbitrary negative initial energy and suitable initial values. Moreover, we give an estimate for the lower and upper bounds of the blow-up time. The main feature of our problems is that the Kirchhoff term may vanish at zero. Finally, we present some recent results for Kirchhoff-type evolution problems involving the fractional Laplacian.
报告人简介：
张彬林，山东科技大学数学与系统科学学院教授，博士生导师。博士毕业于哈尔滨工业大学，先后在意大利地中海研究中心和南开大学陈省身数学研究所做过两站博士后。当前的研究兴趣是变分和拓扑方法及其在数学物理问题中的应用，特别在基尔霍夫型分数阶拉普拉斯方程解的存在性、多解性等方面取得了一系列重要的研究成果。在《Calc. Var. PDEs》、《Nonlinearity》、《J. Differential Equations》、《Disc. Contin. Dyn. Syst.》、《Sci. China Math.》、《Proc. Roy. Soc. Edinb., A》等重要期刊上发表SCI论文100余篇，并担任多个SCI期刊的编委。
