A global approach to fully nonlinear parabolic problems
Authors:
Athanassios G. Kartsatos and Igor V. Skrypnik
Journal:
Trans. Amer. Math. Soc. 352 (2000), 46034640
MSC (1991):
Primary 35K55; Secondary 35K30, 35K35
Published electronically:
June 13, 2000
MathSciNet review:
1694294
Fulltext PDF Free Access
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Abstract: We consider the general initialboundary value problem (1) (2) (3) where is a bounded open set in with sufficiently smooth boundary. The problem (1)(3) is first reduced to the analogous problem in the space with zero initial condition and
The resulting problem is then reduced to the problem where the operator satisfies Condition This reduction is based on a priori estimates which are developed herein for linear parabolic operators with coefficients in Sobolev spaces. The local and global solvability of the operator equation are achieved via topological methods developed by I. V. Skrypnik. Further applications are also given involving relevant coercive problems, as well as Galerkin approximations.
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 P. Acquistapace and B. Terreni, Fully nonlinear parabolic systems, Recent Advances in Nonlinear Elliptic and Parabolic Problems (Nancy, 1988), Pitman Res. Notes in Math., vol. 203, Longman Sci. Tech., Harlow, 1989, pp. 97111. MR 92a:35080
 [2]
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 [3]
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 [4]
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 [5]
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Additional Information
Athanassios G. Kartsatos
Affiliation:
Department of Mathematics, University of South Florida, Tampa, Florida 336205700
Email:
hermes@math.usf.edu
Igor V. Skrypnik
Affiliation:
Institute for Applied Mathematics and Mechanics, R. Luxemburg Str. 74, Donetsk 340114, Ukraine
Email:
skrypnik@iamm.ac.donetsk.ua
DOI:
http://dx.doi.org/10.1090/S0002994700025411
PII:
S 00029947(00)025411
Keywords:
Initialboundary value problem,
mapping of type $(S)_{+},$ Skrypnik's degree theory for demicontinuous mappings of type $(S)_{+},$ Galerkin approximation
Received by editor(s):
April 18, 1997
Received by editor(s) in revised form:
May 7, 1998
Published electronically:
June 13, 2000
Additional Notes:
This research was partially supported by an NSFNRC COBASE grant.
Article copyright:
© Copyright 2000 American Mathematical Society
