Blow-up for semilinear wave equations with the scale invariant damping and super-Fujita exponent
By Ning-An Lai, H. Takamura, Kyouhei Wakasa. 2017
102 citations recorded by the source corpus.
The constant in the scale invariant damping may have a critical value classifying the situation on semilinear wave equations to "heat-like", or to "wave-like". In this paper, we prove a new blow-up result for super Fujita exponent to show that such a critical value has a lower bound which grows up by space dimensions.
Subfields: Control and Systems Engineering, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/bd09fb89f96dab252dd32b7f009681e91951adf2
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In Control and Systems Engineering
In Mathematical Physics
In Statistical and Nonlinear Physics
Citations in the corpus
- Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data (2017, methodology): “the following three figures. 1 3 p µ 5/3 4/3 1 D’Abbicco [3] (SDGE) Our result Wakasugi [13] Figure 1: the case N = 1 1 2 p µ 3 2 1 D’Abbicco [3] (SDGE) Our result Wakasugi [13] D-L-R [4] (SDGE) L-T-W [9] Figure 2: the case N = 2 p 0(2) 4 1 p F(N) p µ µ∗ 2 1 D’Abbicco [3] (SDGE) Our result L-T-W [9] ”
- A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent (2017, background): “In case of dimension n = 1 and µ = 2, Wakasa [10] has verified the critical exponent pc(1) = pF (1) = 3 and showed the optimal of lifespan.”
- Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case (2017, unknown): “Recently, Lai-Takamura-Wakasa [8] applied test function method to obtain following blowup result: T (ε) ≤ Cε, for pF (n) ≤ p < pS(n+ 2μ), n ≥ 2 and 0 < μ < n(2) + n+ 2 2(n+ 2) .”