Initial trace of solutions of semilinear heat equation

Speaker: Laurent Veron (Initial trace of solutions of semilinear heat equation)

Time: 2025-10-17 13:30-14:20
Location: 1510, SIMIS

Abstract: 

We present an overview of the results on the initial trace of positive solutions of
$$\partial_tu− \Delta u + f(u) = 0\quad {\rm in}\  R^N \times (0, T)$$
obtained in the last 20 years. We emphasis the case where
$f(u) = u^p$ with p > 1.

Results show the existence of a critical exponent $p_c = \frac{N+2}{N}$,
which yields to a change the topology on $R^N$ in order to have a complete description of the initial trace when $p ≥ p_c$.

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About Speaker: Laurent Veron，法国杰出教授，法国图尔大学，博士生导师，长期从事非线性分析和偏微分方程的研究，特别是在偏微分问题奇异解方面做出了卓越的贡献。在Invent. Math.、Duke J.、CPAM、JMPA、JEMS等国际数学顶尖杂志发表SCI学术论文200篇。