Asymptotic Behavior of Solutions to the Semilinear Wave Equation with Time-dependent Damping

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Semi‐linear wave models with power non‐linearity and scale‐invariant time‐dependent mass and dissipation (2017, background): “On the contrary, if we are interested in classical damped waves with power non-linearity (even with a special time-dependent coefficient in the dissipation term), then the Fujita exponent comes into play as critical exponent for all dimensions, see [16], [18].”
A competition between Fujita and Strauss type exponents for blow-up of semi-linear wave equations with scale-invariant damping and mass (2019, background): “hod is considered, in [23] it is employed a proper modiﬁcation of the blow-up result for ordinary diﬀerential inequalities introduced ﬁrst in [30] for the constant coeﬃcients case and adapted then in [21] for coeﬃcients b(t) = µ 1(1+t)−β, where β∈ [0,1). Furthermore, in [22] a further nonexistence r”
The Threshold between Effective and Noneffective Damping for Semilinear Waves (2012, background): “special case, a global existence result has been obtained in [16, 19].”
A shift in the Strauss exponent for semilinear wave equations with a not effective damping (2015, background): “-depending critical exponent for (12) for small µ. To complete our overview, we mention that the critical exponent for the wave equation with timedependent damping µhtiκut is 1 + 2/nif κ∈ (−1,1) (see [6, 18, 19]), whereas global existence of small data solutions for p >1 + 2/(n− α) for the wave e”