On the well-posedness and general decay results of Moore-Gibson-Thompson equation with memory

This paper investigates the well-posedness and stability of the solution to Cauchy problem of Moore-Gibson-Thompson equation (MGT for short) with a type-II memory term. First, by applying semigroup method, we show that the Cauchy problem is well-posed under the basic assumptions imposed on the relaxation function g(t) and physical parameters. Then, under the condition alpha beta - tau gamma - alpha integral(infinity)(0) g(s)ds > 0, we establish an estimate of the Fourier image of energy norm, by building some appropriate Lyapunov functionals in Fourier space. Combining Plancherel's theorem and some integral inequalities, we show that the L-2-norm of the energy and solution of the Cauchy problem decay polynomially.