Ukrainian Mathematical Bulletin

Volume 1, Issue 1, 2004 pp. 107-135.

Local Behavior of Solutions of Nonlinear Parabolic Equations in a Domain with Narrow Cavity

Authors: I.V.Skrypnik and M.A.Naumova
Author institution: Institute of Mathematics and Mechanics of the Ukrainian Academy of Sciences, Donetsk, Ukraine, Donetsk National University, Donetsk, Ukraine

Summary: We prove pointwise estimates for model nonlinear parabolic problems in a domain with thin cylindrical cavity. The estimates obtained characterize the dependence of a solution on the thickness of the cavity and serve as a basis for the qualitative investigation of various problems concerning the asymptotic behavior of solutions of nonlinear parabolic equations.

Contents Full-Text PDF