Life-Span of Solutions to Critical Semilinear Wave Equations
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The final open part of the famous Strauss conjecture on semilinear wave equations of the form □u = |u| p , i.e., blow-up theorem for the critical case in high dimensions was solved by Yordanov and Zhang [21], or Zhou [25] independently. But the estimate for the lifespan, the maximal existence time, of solutions was not clarified in both papers. Recently, Takamura and Wakasa [18] have obtained the sharp upper bound of the lifespan of the solution to the critical semilinear wave equations, and their method is based on the method in Yordanov and Zhang [21]. In this paper, we give a much simple proof of the result of Takamura and Wakasa [18] by using the method in Zhou [25] for space dimensions n ≥ 2.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a5eccc1be6e47d740796c5534d28c486dae880a2
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In Applied Mathematics
In Mathematical Physics
Citations in the corpus
- A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent (2017, methodology): “Their proof relies on the use of hypergeometric function, which is initiated from Zhou-Han [13].”
- Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case (2017, methodology): “(22) At this moment, we are at exactly same position as Section 3 of [18].”
- Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data (2017, methodology): “Their approach could be generalized for dealing with the blowup phenomena of the singular problem ∂2t u(x, t) − ∆u(x, t) + V0 |x| ∂tu(x, t) = |u(x, t)| p, (x, t) ∈ RN × (0, T ), u(x, 0) = ε f (x), x ∈ RN , ∂tu(x, 0) = εg(x), x ∈ RN (1.3) with N ≥ 3 and V0 ∈ [0, (N−1) 2 N+1 ) (see [6]) (the techniqu”
- Nonexistence of global solutions for the semilinear Moore – Gibson – Thompson equation in the conservative case (2019, background): “(4) The lifespan of solutions to (3) that blow up in finite time has been intensively considered [26, 47, 48, 49, 27, 9, 41, 52, 40, 15].”