Kakharman N.Zhumabayeva A.2026-04-162026-04-162025Kakharman 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)https://repository.sdu.edu.kz/handle/123456789/2627The 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 theoryendegenerate hyperbolic equationweighted initial conditionwell-posed problemspectral decompositionArticle