On the long time behaviour of solutions to dissipative wave equations inmathbb{R}^{2}

In this paper we present a parabolic approach to studying the diffusive long time behaviour of solutions to the Cauchy problem:

(1)

where u₀ and u₁ satisfy suitable assumptions. After an appropriate scaling we obtain the convergence to a stationary solutio n in L^q norm (1 ≤  q  <  ∞).