I've seen several papers related to the causality condition concerning the viscous wave equation resolution but never understood how causality and stability are linked ? Conceptually, it seems hard to lose causality but even though you break the Kramers-Kroning relations, solutions still exist in a proper space and I can't see why it's a problem, you only lose the uniqueness. And beyond this question, how causality impacts the behavior of a numerical resolution ?
Does someone have could help me out understanding this issue or give me a reference ?
Thanks a lot.
Cheers
P.S : This kind of references http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.309.312 , http://arxiv.org/abs/0901.1226, http://arxiv.org/abs/0808.2354