On a final value problem for a class of nonlinear hyperbolic equations with damping term
On a final value problem for a class of nonlinear hyperbolic equations with damping term
<p style='text-indent:20px;'>This paper deals with the problem of finding the function <inline-formula><tex-math id="M1">\begin{document}$ u(x,t) $\end{document}</tex-math></inline-formula>, <inline-formula><tex-math id="M2">\begin{document}$ (x,t)\in \Omega \times [0,T] $\end{document}</tex-math></inline-formula>, from the final data <inline-formula><tex-math id="M3">\begin{document}$ u(x,T) = g(x) $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M4">\begin{document}$ u_t(x,T) = {h(x)} $\end{document}</tex-math></inline-formula>, <p style='text-indent:20px;'><disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ u_{tt} + a \Delta^2 u_t …