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May 18 at 17:22 comment added Pedro Lauridsen Ribeiro The answer to your question is affirmative by standard local energy estimates, which are proven for your so-called "generalized d'Alembertians" (more generally called nowadays "normally hyperbolic operators") in pretty much the same way as for symmetric hyperbolic systems. The most general proof of this, which holds for the so-called "regularly hyperbolic operators" coming from an Euler-Lagrange variational principle, can be found e.g. in D. Christodoulou's book "The Action Principle and Partial Differential Equations" (Princeton University Press, 2000).
May 18 at 15:56 history edited Dheghom CC BY-SA 4.0
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S May 18 at 15:50 review First questions
May 18 at 16:05
S May 18 at 15:50 history asked Dheghom CC BY-SA 4.0