Preliminaries on fractional parabolic equations

主講人：Chen Wenxiong，紐約Yeshiva大學(xué)終身教授

時(shí)間：2024年7月1日9：30

地點(diǎn)：三號(hào)樓332室

舉辦單位：數(shù)理學(xué)院

主講人介紹：Chen Wenxiong，美國紐約Yeshiva大學(xué)終身教授，數(shù)學(xué)系主任，國際知名的數(shù)學(xué)家。曾多次獲得美國國家科學(xué)基金獎(jiǎng)。擔(dān)任Nonlinear Analysis: Theory, Methods & Applications 及Communications on Pure and Applied Analysis 兩個(gè)SCI數(shù)學(xué)雜志的編輯。研究方向?yàn)榉蔷€性偏微分方程，目前以分?jǐn)?shù)階Laplace方程為主。Chen教授在數(shù)學(xué)頂級(jí)期刊Annals of Math, J. of Diff. Geom., Comm. Pure and Appl. Math, Duke Math. J, Advance in Math, Arch. Rat. Mech. Anal.等發(fā)表論文80余篇，并出版了三本專著，他引已達(dá)五千余次，其中在Duke Math. J.上發(fā)表的名為Classification of solutions of some nonlinear elliptic equations的論文被引高達(dá)1000余次。

內(nèi)容介紹：In this talk, we will introduce various nonlinear fractional parabolic equations Lu = f(t; x; u(x; t)), where L is a fractional parabolic operator assuming the form of ?_t+〖(-?)〗^s, or ?_t^α+〖(-?)〗^s, or 〖(?_t-?)〗^s. Here ?_t^α is the Marchaud fractional derivative and 〖(?_t-?)〗^s is known as the master operator respectively. We will illustrate the extent of non-locality of these operators and explain the differences among them. We prove some simple maximum principles and we illustrate the transition from elliptic problems to parabolic problems.