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

Abstract

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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Article Information

Title	On holomorphic solutions of the heat equation with a Volterra operator coefficient
Source	Methods Funct. Anal. Topology, Vol. 13 (2007), no. 4, 329-332
MathSciNet	MR2374834
Copyright	The Author(s) 2007 (CC BY-SA)

Authors Information

Sergey Gefter
School of Mechanics and Mathematics, Kharkiv National University, 4 Svobody Sq., Kharkiv, 61077, Ukraine 

Citation Example

Sergey Gefter and Anna Vershynina, On holomorphic solutions of the heat equation with a Volterra operator coefficient, Methods Funct. Anal. Topology 13 (2007), no. 4, 329-332.

BibTex

@article {MFAT411,
    AUTHOR = {Gefter, Sergey and Vershynina, Anna},
     TITLE = {On holomorphic solutions of the heat equation with a Volterra operator coefficient},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {13},
      YEAR = {2007},
    NUMBER = {4},
     PAGES = {329-332},
      ISSN = {1029-3531},
  MRNUMBER = {MR2374834},
       URL = {http://mfat.imath.kiev.ua/article/?id=411},
}