Lp-resolvent estimates and time decay for generalized thermoelastic plate equations

Abstract

We consider the Cauchy problem for a coupled system generalizing the thermoelastic plate equations. First we prove resolvent estimates for the stationary operator and conclude the analyticity of the associated semigroup in Lp-spaces, 1 < p < ∞, for certain values of the parameters of the system; here the Newton polygon method is used. Then we prove decay rates of the L^q(ℝn)-norms of solutions, 2 ≤ q ≤ ∞, as time tends to infinity.