Fredholm solvability of a periodic Neumann problem for a linear telegraph equation

• Date: 2013
• Main Authors: Kmit, I. Ya., Кміть, І. Я.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2013
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2425
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We investigate a periodic problem for the linear telegraph equation $$u_{tt} - u_{xx} + 2\mu u_t = f (x, t)$$ with Neumann boundary conditions. We prove that the operator of the problem is modeled by a Fredholm operator of index zero in the scale of Sobolev spaces of periodic functions. This resul...