Fredholm Solvability of a Periodic Neumann Problem for a Linear Telegraph Equation

Author: Kmit I.  

Publisher: Springer Publishing Company

ISSN: 0041-5995

Source: Ukrainian Mathematical Journal, Vol.65, Iss.3, 2013-08, pp. : 423-434

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Abstract

We investigate a periodic problem for a linear telegraph equation 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 in which either μ becomes variable and discontinuous or an additional zero-order term appears. We also show that the solutions of this problem possess smoothing properties.