ACTA MATHEMATICA UNIVERSITATIS COMENIANAE
Vol. LXXV, 2 (2006)
p. 227 - 232
Some applications of parabolic comparison principles to the study of decay estimates
C.-P. Danet
Abstract.
This paper is concerned with the asymptotic behavior of solutions
of general nonlinear parabolic equations. We consider a boundary
value problem which was treated by Reynolds in a classical paper
(J. Diff. Equations 12 (1972), 256-261). Our goal is
to prove by different means a version of the main result in the
above mentioned paper. We also point out that it remains valid
under some weaker hypotheses if the working domain is cylindrical.
Keywords.
Comparison principles, decay estimates.
AMS Subject classification. 35B40.
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