Parabolic Type Decay Rates for 1-D-Thermoelastic Systems with Time-Dependent Coefficients

 The purpose of this paper is to derive L ^p − L ^q decay estimates for linear thermoelastic systems with time-dependent coefficient in one space variable. When all coefficients in the system have the same growth speed with small oscillations, we obtain a parabolic type decay estimate. For the system with time-dependent coefficients, we need to investigate the delicate asymptotic behaviour of characteristic roots and the remainder of diagonalization, which will be treated by dividing the phase space into three regions. Received September 15, 2001; in revised form April 20, 2002