  The research monograph expounds the foundation of a new theory of parabolic
initial-boundary-value problems in scales of generalized anisotropic Sobolev
spaces. These scales are calibrated essentially more finely with the help of a
function parameter of regularity than the classes of spaces used earlier in the
theory of parabolic problems. The monograph is featured by the systematic
application of the method of quadratic interpolation (with function parameter)
between abstract and Sobolev inner product spaces.
  The monograph is intended for the researches, professors, PhD students, and
senior students specializing in differential equations and mathematical
analysis.
