On Kinds of Weak Solutions to an Initial Boundary Value Problem for 1D Linear Degenerate Wave Equation
In this article, we discuss the existence and uniqueness of mild, variational, and the so-called non-variational solutions to an initial-boundary value problem (IBVP) for linear wave equation with strong interior degeneracy of the coefficient in the principal part of the elliptic operator. The objec...
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| Date: | 2025 |
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| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Фізико-технічний інститут низьких температур ім. Б.І. Вєркіна Національної академії наук України
2025
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| Subjects: | |
| Online Access: | https://jmag.ilt.kharkiv.ua/index.php/jmag/article/view/1090 |
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| Journal Title: | Journal of Mathematical Physics, Analysis, Geometry |
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Journal of Mathematical Physics, Analysis, Geometry| Summary: | In this article, we discuss the existence and uniqueness of mild, variational, and the so-called non-variational solutions to an initial-boundary value problem (IBVP) for linear wave equation with strong interior degeneracy of the coefficient in the principal part of the elliptic operator. The objective is to provide a well-posedness analysis of the IBVP and find out how the density property of smooth functions in the corresponding weighted Sobolev space affects the uniqueness of its solutions. We show that, in general, the uniqueness of solutions may be violated if the 'degree of degeneracy' corresponds to the strong degeneracy case.
Mathematical Subject Classification 2020:35L80, 35D30 |
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