Global solutions with asymptotic self-similar behaviour for the cubic wave equation

2023/04/19 by Duyckaerts, Thomas, Negro, Giuseppe · 1 citation
#35L05 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2304.09567

Abstract

We construct a two-parameter family of explicit solutions to the cubic wave equation on ℝ¹⁺³. Depending on the value of the parameters, these solutions either scatter to linear, blow-up in finite time, or exhibit a new type of threshold behaviour which we characterize precisely.

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• Blow-up, decay, and convergence to equilibrium for focusing damped cubic Klein-Gordon and Duffing equations

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