Well-Posedness for a Degenerate Hyperbolic Equation with Weighted Initial Data

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dc.contributor.authorKakharman N.
dc.contributor.authorZhumabayeva A.
dc.date.accessioned2026-04-16T06:35:23Z
dc.date.available2026-04-16T06:35:23Z
dc.date.issued2025
dc.description.abstractThe focus of this study is an initial-boundary value problem associated with the degenerate hyperbolic equation t∂ttu + 1 2 ∂tu − ∆u = g in a bounded domain. Due to the singularity at t = 0, standard initial conditions lead to an ill-posed problem. To achieve solvability of the problem, we introduce a ”modified” Cauchy problem using weighted initial conditions for this degeneracy. The main result of the study is the proof of the well-posedness of this problem within the framework of classical Sobolev spaces, as well as the obtaining of a priori estimates of the solution. Furthermore, the general boundary conditions for the one-dimensional equation were derived by using the restriction and extension theory
dc.identifier.citationKakharman N , Zhumabayeva A / Well-Posedness for a Degenerate Hyperbolic Equation with Weighted Initial Data / SDU University / Journal of Emerging Technologies and Computing (JETC), Vol. 3 No. 3 (2025)
dc.identifier.urihttps://repository.sdu.edu.kz/handle/123456789/2627
dc.language.isoen
dc.publisherSDU University
dc.subjectdegenerate hyperbolic equation
dc.subjectweighted initial condition
dc.subjectwell-posed problem
dc.subjectspectral decomposition
dc.titleWell-Posedness for a Degenerate Hyperbolic Equation with Weighted Initial Data
dc.typeArticle

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