Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 48, pp. 1-12.

Title: High regularity of the solution of a nonlinear parabolic
       boundary-value problem
   
Authors: Luminita Barbu (Ovidius Univ., Romania)
         Gheorghe Morosanu (Al. I. Cuza  Univ., Romania)
         Wolfgang L. Wendland (Univ. of Stuttgart, Germany)
         
Abstract: 
  The aim of this paper is to report some results concerning
  high regularity of the solution  of a nonlinear parabolic
  problem with a linear parabolic differential equation in
  one spatial dimension and nonlinear boundary conditions.
  We show that any regularity can be reached provided that
  appropriate smoothness of the data and compatibility
  assumptions are required.
  
Submitted April 11, 2002.  Published May 29, 2002.
Math Subject Classifications: 35K60, 35K05, 35K20, 34G20, 47H05, 47H20.
Key Words: Parabolic equation; nonlinear boundary conditions; 
           maximal monotone operator; subdifferential;
           compatibility conditions.