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Complex analysis and mathematical physics
October 17, 2017 16:00–18:00, Moscow, Steklov Mathematical Institute, Room 430 (8 Gubkina)
 


On solubility of characteristic Cauchy problems

A. V. Domrin

Lomonosov Moscow State University

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Abstract: Under which conditions on a holomorphic germ $u(x)$ at a point $x_0\in\mathbb C$ can one find a holomorphic germ $u(x,t)$ at a point $(x_0,t_0)\in\mathbb C^2$ satsifying an evolution equation $u_t=F[u]$ in a neighbourhood of this point (where $F[u]$ is a prescribed polynomial in $u$ and its partial derivatives with respect to $x$) and the initial condition $u(x,t_0)=u_0(x)$? We shall present classical results (surprising and not well-known) that completely answer this question in the case when the differential polynomial $F[u]$ is linear, as well as some recent advances in this problem.
 
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