2022/06/28 by Piske, Alessandra, Charão, Ruy Coimbra, Ikehata, Ryo
#35L05 #35R12 #35S05 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary 35B4 #Secondaryn 35B20
paper · doi:10.48550/arxiv.2206.13713
We consider strongly damped wave equations with logarithmic mass-like terms with a parameter θ∈ (0; 1]. This research is a part of a series of wave equations that was initiated by Charão-Ikehata [6], Charão-D'Abbicco-Ikehata considered in [5] depending on a parameter θ∈ (1/2,1) and Piske- Charão-Ikehata [26] for small parameter θ∈ (0,1/2). We derive a leading term (as time goes to infinity) of the solution, and by using it, a growth and a decay property of the solution itself can be precisely studied in terms of L2-norm. An interesting aspect appears in the case of n = 1, roughly speaking, a small θ produces a diffusive property, and a large θ gives a kind of singularity, expressed by growth rates.