Well-Posedness for a Degenerate Hyperbolic Equation with Weighted Initial Data
No Thumbnail Available
Date
2025
Authors
Journal Title
Journal ISSN
Volume Title
Publisher
SDU University
Abstract
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
Description
Keywords
degenerate hyperbolic equation, weighted initial condition, well-posed problem, spectral decomposition
Citation
Kakharman 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)