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

### Abstract

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 result is stable under small perturbations of the equation where p becomes variable and discontinuous or an additional zero-order term appears. We also show that the solutions of this problem possess smoothing properties.
Published

25.03.2013

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 65, no. 3, Mar. 2013, pp. 381-9, https://umj.imath.kiev.ua/index.php/umj/article/view/2425.

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Section

Research articles