Gevrey Problem for a Mixed Parabolic Equation with a Singular Coefficient

In this paper, we examine the unique solvability of the Gevrey problem for a mixed parabolic equation with singular coefficients in a band. We prove the existence and uniqueness of a solution to the problem stated. The uniqueness of a solution is proved by the method of energy integrals and the exis...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 254; no. 6; pp. 718 - 730
Main Author Mamanazarov, A. O.
Format Journal Article
LanguageEnglish
Published New York Springer US 02.05.2021
Springer
Springer Nature B.V
Subjects
Differential equations
Mathematics
Mathematics and Statistics
Singular integral equations
Uniqueness
singular coefficient
35K20
mixed-parabolic equation
35A01
existence of solution
uniqueness of solution
Gevrey problem
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-021-05335-0

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Summary:In this paper, we examine the unique solvability of the Gevrey problem for a mixed parabolic equation with singular coefficients in a band. We prove the existence and uniqueness of a solution to the problem stated. The uniqueness of a solution is proved by the method of energy integrals and the existence by methods of the theory of Volterra, Fredholm, and singular integral equations.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-021-05335-0