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

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Ukrainian Mathematical Journal Aims and scope

We investigate a periodic problem for a linear telegraph equation

$$ {u_{tt }}-{u_{xx }}+\mu {u_t}=f(x,t) $$

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 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.

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Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 65, No. 3, pp. 381–391, March, 2013.

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Kmit, I. Fredholm Solvability of a Periodic Neumann Problem for a Linear Telegraph Equation. Ukr Math J 65, 423–434 (2013). https://doi.org/10.1007/s11253-013-0786-6

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  • DOI: https://doi.org/10.1007/s11253-013-0786-6

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