Boundary-Value Problems for Ultraparabolic and Quasi-Ultraparabolic Equations with Alternating Direction of Evolution

We examine the solvability of boundary-value problems for the differential equation h t u t + − 1 m D a 2 m + 1 u − Δu + c x t a u = f x t a ; x ∈ Ω ⊂ ℝ n , 0 < t < T , 0 < a < A , D a k = ∂ k ∂ a k , where the sign of the function h ( t ) arbitrarily alternates in the interval [0 , T ]....

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Bibliographic Details
Published in:Journal of mathematical sciences (New York, N.Y.) N.Y.), 2020-11, Vol.250 (5), p.772-779
Main Author: Kozhanov, A. I.
Format: Article
Language:English
Subjects:
Boundary value problems
Differential equations
Existence theorems
Mathematical analysis
Mathematics
Mathematics and Statistics
Uniqueness theorems
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Summary:We examine the solvability of boundary-value problems for the differential equation h t u t + − 1 m D a 2 m + 1 u − Δu + c x t a u = f x t a ; x ∈ Ω ⊂ ℝ n , 0 < t < T , 0 < a < A , D a k = ∂ k ∂ a k , where the sign of the function h ( t ) arbitrarily alternates in the interval [0 , T ]. The existence and uniqueness theorems of regular (i.e., possessing all generalized derivatives in the Sobolev sense) solutions are proved.
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05042-2