Critical exponent for the semilinear wave equation with scale invariant damping

By Yuta Wakasugi. 2012

70 citations recorded by the source corpus.

In this paper we consider the critical exponent problem for the semilinear damped wave equation with time-dependent coefficients. We treat the scale invariant cases. In this case the asymptotic behavior of the solution is very delicate and the size of coefficient plays an essential role. We shall prove that if the power of the nonlinearity is greater than the Fujita exponent, then there exists a unique global solution with small data, provided that the size of the coefficient is sufficiently large. We shall also prove some blow-up results even in the case that the coefficient is sufficiently small.

Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/72901012c76b71a51bdf9341ae2ccc0f4c5c6b77

Citations in the corpus

• Life-span of solutions to semilinear wave equation with time-dependent critical damping for specially localized initial data (2017, unknown): “in [14,15], and { 1 < p ≤ pF (N ) for N = 1, μ = 2, 1 < p < p0(N + 2) for N = 2, 3, μ = 2,”
• Life-span of semilinear wave equations with scale-invariant damping: Critical Strauss exponent case (2017, unknown): “However, combing the result of [2] and [13], there is still gaps.”
• A note on the blowup of scale invariant damping wave equation with sub-Strauss exponent (2017, unknown): “Wakasugi [8] has obtained the blowup result if 1 < p ≤ pF (n) and µ > 1, or 1 p ≤ 1 + 2n+µ−1 and 0 µ ≤ 1.”