This article is cited in 2 papers

First order hyperbolic equations with constant operator coefficients

E. A. Fadeeva


Abstract: This paper considers the Cauchy problem for a hyperbolic equation with constant operator coefficients in Hilbert space:
$$ \frac{\partial\psi}{\partial t}=\sum_{k=1}^n A_k\frac{\partial\psi}{\partial x_k}+B\psi, $$
where $A_k$ and $B$ are selfadjoint operators and $B$ is semibounded.
As an example we consider ultraparabolic systems.
Bibliography: 10 titles.

UDC: 517.945

MSC: Primary 35L45; Secondary 35K45, 35R15, 47D05, 47B44

Received: 16.03.1973 and 06.08.1973

 English version: Mathematics of the USSR-Sbornik, 1974, 22:2, 257–270

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