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This paper considers the hyperbolic-parabolic coupled system, arising fromthe generalized thermoelastic coupled system, in the whole space$\mathbb{R}^n$. We study some qualitative properties for an energy term bydiagonalization procedures, and for the solution by the WKB analysis.Particularly, we derive new large time asymptotic profiles with theregularity-loss structure (from the biharmonic parabolic equation and thediffusion wave equation with the Riesz potential operator) and optimal decayestimates with suitable higher regularities for the Cauchy data. Finally, wediscover that the wave equation with the Riesz potential dissipation is a largetime approximated model of our hyperbolic-parabolic coupled system.

Large time behavior for the hyperbolic-parabolic coupled system with the regularity-loss structure