@article{Djaouti2023, 
author = {Abdelhamid Mohammed Djaouti and Michael Reissig},
title = {Critical regularity of nonlinearities in semilinear effectively damped wave models},
year = {2023},
journal = {AIMS Mathematics},
volume = {8},
number = {2},
pages = {4764-4785},
keywords = {blow-up, global existence, damped wave equations, time dependent dissipation, critical regularity},
url = {https://www.sciopen.com/article/10.3934/math.2023236},
doi = {10.3934/math.2023236},
abstract = {In this paper we consider the Cauchy problem for the semilinear effectively damped wave equation         u          t      t        −      u          x      x        +  b  (  t  )      u          t        =      |    u            |              3        μ  (      |    u      |    )  ,        u  (  0  ,  x  )  =      u          0        (  x  )  ,            u          t        (  0  ,  x  )  =      u          1        (  x  )  .Our goal is to propose sharp conditions on    μ to obtain a threshold between global (in time) existence of small data Sobolev solutions (stability of the zero solution) and blow-up behaviour even of small data Sobolev solutions.}
}