On the Stabilization Rate of Solutions of the Cauchy Problem for a Parabolic Equation with Lower-Order Terms

The following Cauchy problem for parabolic equations is considered in the half-space D ¯ = ℝ N × 0 ∞ , N ≥ 3: L 1 u ≡ Lu + c x t u − u t = 0 , x t ∈ D , u x 0 = u 0 x , x ∈ ℝ N . It is proved that for any bounded and continuous in ℝ N initial function u 0 ( x ) , the solution of the above Cauchy pro...

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2018-09, Vol.233 (6), p.807-827
Main Author: Denisov, V. N.
Format: Article
Language:English
Subjects:
Cauchy problems
Continuity (mathematics)
Half spaces
Mathematics
Mathematics and Statistics
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Summary:The following Cauchy problem for parabolic equations is considered in the half-space D ¯ = ℝ N × 0 ∞ , N ≥ 3: L 1 u ≡ Lu + c x t u − u t = 0 , x t ∈ D , u x 0 = u 0 x , x ∈ ℝ N . It is proved that for any bounded and continuous in ℝ N initial function u 0 ( x ) , the solution of the above Cauchy problem stabilizes to zero uniformly with respect to x from any compact set K in ℝ N either exponentially or as a power (depending on the estimate for the coefficient c ( x, t ) of the equation).
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-018-3968-9