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The family of Jordan-Moore-Gibson-Thompson (JMGT) equations arises innonlinear acoustics when a relaxed version of the heat flux law is employedwithin the system of governing equations of sound motion. Motivated by thepropagation of sound waves in complex media with anomalous diffusion, weconsider here a generalized class of such equations involving two (weakly)singular memory kernels in the principal and non-leading terms. To relate themto the second-order wave equations, we investigate their vanishing relaxationtime behavior. The key component of this singular limit analysis are theuniform bounds for the solutions of these nonlinear equations of fractionaltype with respect to the relaxation time. Their availability turns out todepend not only on the regularity and coercivity properties of the two kernels,but also on their behavior relative to each other and the type of nonlinearitypresent in the equations.

The vanishing relaxation time behavior of multi-term nonlocal Jordan-Moore-Gibson-Thompson equations