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)


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”.


Strong Solution Borel Measure Functional Space Energy Inequality Hopf Equation 
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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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