A dynamical system approach to the Emden-Chandrasekar-Ricatti equation

Speaker:Marie-Françoise BIDAUT-VERON (Institut Denis Poisson-CNRS UMR 7013 Universite de Tours)

Time: 2025-10-17 14:30-15:20
Location: R1510, SIMIS

摘要：
We study the solutions of the equation
$$-\Delta u+m |\nabla u|^q=e^u\quad {\rm in}\ R^N\setminus{0} $$
with $m > 0$. Here we are concerned by the radial solutions of any sign: we
give a complete description of their asymptotic behaviour near the singularity
0; or near 1, according to the cases $q < 2$ or $q > 2$.
We focuss on the existence results of local or global solutions, showing that all the possible types of singular solutions, of eikonal type, Emden type or Hamilton-Jacobi type do exist, and we study their possible uniqueness. The proofs use several techniques inherited from the theory of dynamical systems of order 2 and 3. Some of the results of this paper are still open in the nonradial case.

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About Speaker:
Marie Francoise Bidaut-Veron，法国图尔大学教授，博士生导师，主要从事偏微分方程的研究，对拟线性p拉普拉斯问题做了一系列重要的工作。在Invent. Math.、Math. Ann.、CPAM、JMPA、CVPDE等国际数学顶尖杂志发表SCI学术论文82篇。