Necessary and Sufficient Conditions of Stabilization of Solutions of the First Boundary-Value Problem for a Parabolic Equation

Necessary and sufficient conditions are established for the stabilization of the solution of the first boundary-value problem for a divergent second-order parabolic equation with no lower-order terms. For an arbitrary (possibly unbounded) domain Q ⊂ ℝ N , N  ≥ 3, with an initial function u 0 ( x ) d...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2014-03, Vol.197 (3), p.303-324
Main Author: Denisov, V. N.
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:Necessary and sufficient conditions are established for the stabilization of the solution of the first boundary-value problem for a divergent second-order parabolic equation with no lower-order terms. For an arbitrary (possibly unbounded) domain Q ⊂ ℝ N , N  ≥ 3, with an initial function u 0 ( x ) defined in Q for t  = 0, one studies the influence of Q on the stabilization of the solution in the cylinder Z  =  Q  × [0,∞) with the homogeneous boundary conditions on the lateral surface of Z .
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-014-1716-3