I know that Wave equation doesn't satisfy maximum principle but I have also heard that hyperbolic equations have no maximum principle. But I don't know any reference or proof regarding that. It would be really helpful if I get a help or resource regarding the same. 

And second question is , I have also heard in one of the lectures that subsolutions cannot touch even tangentially because of strong maximum principle and weak maximum principle says that subsolution doesn't intersect each other. How I don't get to see this geometry behind the weak solution. Any help is very much appreciated.