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A tiny step towards a theory of functional derivative equations —A strong solution of the space-time hopf equation

  • Atsushi Inoue
Statistical Methods
Part of the Lecture Notes in Mathematics book series (LNM, volume 1530)

Abstract

In this note, we construct a strong solution of the space-time Hopf equation,
$$(\frac{\partial }{{\partial t}} - v\Delta )\frac{{\delta Z(\eta )}}{{\delta \eta _\ell (x,t)}} = i\left[ {\tilde T^* \left\{ {\frac{{\delta ^2 Z(\eta )}}{{\delta \eta _j (x,t)\delta \eta _k (x,t)}}} \right\}} \right]^\ell + if^\ell (x,t)Z(\eta )$$
with certain subsidary conditions, which is an example of functional derivative equations and is manageable using a tiny part of “analysis in functional spaces”.

Keywords

Strong Solution Borel Measure Functional Space Energy Inequality Hopf Equation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1992

Authors and Affiliations

  • Atsushi Inoue
    • 1
  1. 1.Department of MathematicsTokyo Institute of TechnologyJapan

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