2017
Том 69
№ 9

All Issues

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

Kmit I. Ya.

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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.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 3, pp 423-434.

Citation Example: Kmit I. Ya. Fredholm solvability of a periodic Neumann problem for a linear telegraph equation // Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 381-391.

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