Please provide me with sufficient conditions to guarantee a unique periodic solution of the linear telegraph equation. I am interested in linear telegraph not in the nonlinear cases.
Have a look at the paper below:
https://www.sciencedirect.com/science/article/abs/pii/S0362546X97004781
The linear case is a particular case of that discussed in the paper above, by simply letting $h(x,u) = 0$ for all $x$ and $u$.
Hope this helps.
This links have good information
https://www.hindawi.com/journals/mpe/2018/2805161
I think this paper is a good source:
Article Periodic solutions of parabolic and telegraph equations with...
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