Parabolic type decay rates for 1-d-thermoelastic systems with time-dependent coefficients (Q1404227)

The aim of this paper is to study the linear 1D thermoelastic system, a hyperbolic-parabolic coupled system with time dependent coefficients, and to analyse the influence of coefficients on the \(L^p\)-\(L^q\) decay estimate. All coefficients in the system have same growth speed with small oscillations. A pointwise estimate for the Fourier transform of a vector related to the solutions is proven. In the estimate, there appears a term which is connected with the characteristic roots of the 1D thermoelastic system. The asymptotics of characteristic roots are also analysed by the use of the above-mentioned term.