Electronic Journal of Differential Equations, Vol. 2021 (2021), No. 73, pp. 1-9.

Title: Decay estimates for solutions of evolutionary damped p-Laplace equations
       
Authors: Farid Bozorgnia (Univ. of Lisbon, Portugal)
         Peter Lewintan (Univ. of Duisburg-Essen, Germany)

Abstract:
 In this note, we study the asymptotic behavior, as t tends to infinity,
 of the solution u to the evolutionary damped p-Laplace equation
 $$
  u_{tt}+ u_t =\Delta_p u
 $$
 with  Dirichlet boundary conditions.  Let u<sup>*</sup> denote the stationary solution with
 same boundary values, then we prove  the W<sup>1,p</sup>-norm of u(t) - u<sup>*</sup> decays
 for large t like t<sup>-1/((p-1)p)</sup>, in the degenerate case p&gt;2.

Submitted July 8, 2021. Published September 10, 2021.
Math Subject Classifications: 35B40, 35L70.
Key Words: p-Laplace; telegraph equation; asymptotic behavior; convexity.