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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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 250; no. 5; pp. 772 - 779
Main Author Kozhanov, A. I.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2020
Springer
Springer Nature B.V
Subjects
Boundary value problems
Differential equations
Existence theorems
Mathematical analysis
Mathematics
Mathematics and Statistics
Uniqueness theorems
regular solution
uniqueness
35K70
existence
ultraparabolic equation
35M99
boundary-value problem
odd-order nonclassical differential equation with alternating direction of evolution
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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.
Bibliography:ObjectType-Article-1
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-020-05042-2