Abstract
We consider the Cauchy problem in R n for the so-called σ-evolution equations with damping terms. We derive asymptotic profiles of solutions with weighted L 1 , 1 ( R n ) initial data, and investigates the optimality of estimates of solutions in L 2 -sense. The obtained results will generalize and compensate those already known in (J. Math. Anal. Appl. 478 (2019) 476–498, J. Diff. Eqns 257 (2014) 2159–2177, Diff. Int. Eqns 30 (2017), 505–520).
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