Browsing by Author "Kakharman N."

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    Well-Posedness for a Degenerate Hyperbolic Equation with Weighted Initial Data
    (SDU University, 2025) Kakharman N.; Zhumabayeva A.
    The 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