Abstract
In this paper we study the Cauchy problem for doubly dissipative elastic waves in two space dimensions, where two different damping terms consist of friction or structural damping. We derive energy estimates and diffusion phenomena with different assumptions on initial data. Particularly, we find a new threshold for the influence from different damping on diffusion phenomena. Additionally, optimal decay estimates of solution from the above and the below in a weighted L1 framework are obtained.
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