On the Cauchy Problem for the Wave Equation in a Two-Dimensional Domain with Data on the Boundary

The subject of the present paper is the Cauchy problem for the wave equation in a space-time cylinder Ω × ℝ, Ω ⊂ ℝ 2 , with data on the surface ∂Ω × I, where I is a finite time interval. The algorithm for solving the Cauchy problem with data on S × I, S ⊂ ∂Ω, was obtained previously. Here we adapt t...

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Bibliographic Details
Published inJournal of mathematical sciences (New York, N.Y.) Vol. 277; no. 4; pp. 575 - 585
Main Author Demchenko, M. N.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 15.12.2023
Springer
Springer Nature B.V
Subjects
Algorithms
Analysis
Cauchy problems
Mathematics
Mathematics and Statistics
Wave equations
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Summary:The subject of the present paper is the Cauchy problem for the wave equation in a space-time cylinder Ω × ℝ, Ω ⊂ ℝ 2 , with data on the surface ∂Ω × I, where I is a finite time interval. The algorithm for solving the Cauchy problem with data on S × I, S ⊂ ∂Ω, was obtained previously. Here we adapt this algorithm to the special case S = ∂Ω and show that the solution in this situation is determined with higher stability in comparison with the case S ⊂ ≠ ∂Ω.
Bibliography:ObjectType-Article-1
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content type line 14
ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06864-6