Aliev, Akbar B.; Shafieva, Gulshan Kh. Mixed problem with dynamical transmission condition for a one-dimensional hyperbolic equation with strong dissipation. (English) Zbl 1471.35195 Math. Methods Appl. Sci. 44, No. 8, 7121-7133 (2021). Summary: In this paper, we study a mixed problem for the nonlinear hyperbolic equation with a strong dissipation and a dynamical transmission condition. The existence and uniqueness theorems of local and global solutions are proved. MSC: 35L53 Initial-boundary value problems for second-order hyperbolic systems 35L71 Second-order semilinear hyperbolic equations 35B40 Asymptotic behavior of solutions to PDEs Keywords:dynamical transmission condition; global solution; mixed problem; strongly damped wave equation PDFBibTeX XMLCite \textit{A. B. Aliev} and \textit{G. Kh. Shafieva}, Math. Methods Appl. Sci. 44, No. 8, 7121--7133 (2021; Zbl 1471.35195) Full Text: DOI