分野別セミナー

We consider the linearized hyperbolic-parabolic coupled systems, which describe heat-conductive materials having the properties of elasticity and viscosity. These systems contain the nonlinear viscoelastic systems and the total energy balance equation. In this talk, we present the results obtained for the decay property of the aforementioned systems. Appealing to the pointwise estimate in the Fourier space, we obtain decay estimates of solutions using the method developed by Prof. Kawashima, provided that the initial data are in L 2 ∩ L 1 . Moreover, we obtain enegy estimate for linear solutions, decay property for solution operators and pointwise estimates of the fundamental solutions in the Fourier space. This talk is based on the joint research work with Professors S. Kawashima, T. Ogawa and J. Segata.

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