题  目：New Kind of Observations in an Inverse arabolic Problem

报告人： Cristofol Michel, Aix-Marseille University Marseille, France

时  间：2015年1月28日     上午 9:30-10:30

地  点：管理科研楼 1218室

报告摘要：

In this talk, I analyze the inverse problem of determining the reaction term $f(x, u)$ in reaction-di usion equations of the form $/partial_t u-D/partial_{xx}u = f(x, u)$, where $f$ is assumed to be periodic with respect to $x/in /mathbb{R}$. Starting from a family of exponentially decaying initial conditions $u_{0, /lambda}$, I will show that the solutions $u_{/lambda}$ of this equation propagate with constant asymptotic spreading speeds $w_{/lambda}$. The main result shows that the linearization of $f$ around the steady state $0$, $/partial_u f(x, 0)$, is uniquely determined (up to a symmetry) among a subset of piecewise linear functions, by the observation of the asymptotic spreading speeds $w_{/lambda}$.

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