In this article, we are interested by a system of heat equations with initial condition and zero Dirichlet boundary conditions. We prove a finite‐time blow‐up result for a large class of solutions with positive initial energy.

Here, a system of 3 wave equations in Rn with infinite memories acting in the first 2 equations is considered. Using weighted spaces, we prove the polynomial stability of the system under some conditions on μ1,μ2, and ϕ as t→∞.

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