Electron. J. Diff. Eqns., Vol. 2002(2002), No. 48, pp. 1-12.

High regularity of the solution of a nonlinear parabolic boundary-value problem

Luminita Barbu, Gheorghe Morosanu, & Wolfgang L. Wendland

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.

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Luminita Barbu
Department of Mathematics and Informatics
Ovidius University
Blvd. Mamaia 124
8700 Constan\c ta, Romania
e-mail: lbarbu@univ-ovidius.ro
Gheorghe Morosanu
Department of Mathematics
``Al. I. Cuza'' University
Blvd. Carol I, 11
6600 Iasi, Romania
e-mail: gmoro@uaic.ro
Wolfgang L. Wendland
Mathematisches Institut A
University of Stuttgart
Pfaffenwaldring 57
70569 Stuttgart, Germany
e-mail: wendland@mathematik.uni-stuttgart.de

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