S. Gefter

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Articles: 1

On holomorphic solutions of the heat equation with a Volterra operator coefficient

MFAT 13 (2007), no. 4, 329-332

329-332

Let $A$ be a bounded operator on a Hilbert space and $g$ a vector-valued function, which is holomorphic in a neighborhood of zero. The question about existence of holomorphic solutions of the Cauchy problem $\left\{ \begin{array}{ll} \displaystyle\frac{\partial u}{\partial t}= A\displaystyle\frac{\partial^{2}u}{\partial x^2}\\ u(0,x)=g(x) \\ \end{array} \right.$ is considered in the paper.

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