Asymptotically self-similar global solutions of a damped wave equation with nonlinear memory (Q2852327)

For the considered damped wave equation with nonlinear memory, the global existence of solutions has been studied in [\textit{A. Z. Fino}, Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 74, No. 16, 5495--5505 (2011; Zbl 1222.35025)], where the global existence of solutions has been proved. Under some very special assumptions on model parameters and for space dimension smaller than 4, the existence of a unique global mild solution for the Cauchy problem is proved. Under some additional conditions, one shows that some small initial data could lead to global solutions which are asymptotic to the self-similar solutions of the corresponding heat equation.