题目: A heat equation with exponential nonlinearity and with singular initial data in R^2

报告人: Prof. Bernhard Heinrich Ruf (Istituto Lombardo, Accademia di Scienze e Lettere)

时间: 2024年6月7日，周五下午，14:00-15:00

地点: 立德楼701

腾讯会议: 563602060， 密码: 2024

摘要: We consider a semilinear heat equation with exponential nonlinearities and with singular initial data in R^2.

In R^n, n≥3, critical growth related to singular initial data is polynomial and has been studied by several authors. Indeed, existence and non-existence results for singular initial data in suitable L^p-spaces were obtained by Weissler and Brezis--Cazenave; furthermore, non-uniqueness results for certain singular initial data were given by Ni--Sacks and Terraneo.

In dimension n=2 critical growth is given by nonlinearities of exponential type (cf. Trudinger--Moser). We prove that similar phenomena as in R^n, n≥3, namely existence, non-existence and non-uniqueness, occur for suitable exponential nonlinearities and for singular initial data belonging to certain Orlicz spaces.

报告人简介: Bernhard Ruf is a Professor at Istituto Lombardo, Accademia di Scienze e Lettere, Milano, Italy. His research interests include Nonlinear Analysis, Nonlinear Partial Differential Equations, Calculus of Variations, Singularity Theory and Bifurcation. He serves as an eidtorial board member for Milan J. Math., Nonlinear Anal., DCDS. Additionally, he had organized the Leonardo da Vinci Lectures and he has contributed to esteemed journals such as Comm. Pure Appl. Math., J. Eur. Math. Soc., J. Reine Angew. Math., Ann. Inst. H. Poincaré C Anal. Non Linéaire, Indiana Univ. Math. J., Arch. Rational Mech. Anal., J. Funct. Anal., Calc. Var. Partial Differential Equations, etc.

报告人：Bernhard Ruf之前是米兰大学数学学院的教授，现为伦巴第学院科学与文学院的全职教授。他的研究兴趣包括非线性分析，非线性偏微分方程，变分法，奇异和分歧理论等。他是 Milan J. Math., Nonlinear Anal., DCDS 等杂志的编委或主编。他曾经主办达芬奇讲座，并且已经在 Comm. Pure Appl. Math., J. Eur. Math. Soc., J. Reine Angew. Math., Ann. Inst. H. Poincaré C Anal. Non Linéaire, Indiana Univ. Math. J., Arch. Rational Mech. Anal., J. Funct. Anal., 等国际知名杂志发表数篇学术论文。

伦巴第学院简介：伦巴第学院科学与文学院（Istituto Lombardo, Accademia di Scienze e Lettere），扎根于米兰及其所在的伦巴第地区已有两个多世纪的悠久历史。该学院的建立可以追溯到1797年，由拿破仑·波拿巴在意大利共和国宪法中的第297条所规定，旨在模仿法兰西学院的模式，负责收集并完善艺术与科学的发现。1810年，拿破仑设立了皇家研究所总部，使得该学院成为了科学、文学和艺术的中心，与布雷拉宫相连。1838年，随着拿破仑的垮台，该学院的名称变更为伦巴第-威尼托王国的帝国皇家研究所科学、文学和艺术。1859年，该学院移交给了意大利政府，并开始了新的章程。从1935年起，该学院不再由国家所有，成为了一个自治机构，但仍受到教育部的监管。1959年，该学院更名为伦巴第科学与文学院，并迁至兰德里亚尼宫，延续了其悠久的学术传统。该学院的成员曾包括诸如拿破仑、亚历山德罗·沃尔塔、卡米洛·高尔基等杰出人士，同时也培养了四位诺贝尔奖获得者。