Fredholm Solvability of Periodic Neumann Problem for a Linear Telegraph Equation

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

2011-06-08

arxiv.org/abs/1106.1517v1

Mathematics

Analysis of PDEs

12 pages

Scientific paper

We investigate the linear telegraph equation $$ u_{tt}-u_{xx}+2\mu u_t=f(x,t) $$ with periodic Neumann boundary conditions. We prove that the operator of the problem is modeled as a Fredholm operator of index zero in the scale of Sobolev-type spaces of periodic functions. This result extends to small perturbations of the equation where $\mu$ becomes variable and discontinuous or an additional zero-order term appears. We also show that the solutions to the problem are smoothing.

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