Title: Asymptotic Methods in Analysis
Speaker: Fudong Wang
Date: Thursday, 27th August.
Time: 2:00 pm
Abstract: In this talk, I will introduce the history of several well-known asymptotic methods in analysis. Then we will apply those methods via examples. The first example would be to apply Laplace’s method to get one of the oldest asymptotic results, the Stirling’s formula, i.e. $$n!\sim e^{-n}n^n\sqrt{2\pi n},n\rightarrow \infty.$$ Next example is to apply the saddle point method to get the asymptotic of the integral $$\int_{\mathbb{R}}f(z)e^{it(z^2+z)}dz,\quad t\rightarrow \infty .$$ Then I will introduce one recently developed asymptotic method called $\bar{\partial}-$steepest descent method, and apply it to study the long-time asymptotic for the linear Schrödinger equation: $$ iu_t+u_{xx}=0,\quad u(x,0)=q(x)\in H^1(\mathbb{R}). $$
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