Existence of solutions to the semilinear damped wave equation with non-L² slowly decaying data : polynomial nonlinearity case

2025/05/16 by Ikeda, Masahiro, Inui, Takahisa, Wakasugi, Yuta
#35A01 #35L71 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.10768

Abstract

We study the Cauchy problem of the semilinear damped wave equation with polynomial nonlinearity, and establish the local and global existence of the solution for slowly decaying initial data not belonging to L²(ℝⁿ) in general. Our approach is based on the L^p-L^q estimates of linear solutions and the fractional Leibniz rule in suitable homogeneous Besov spaces.

Citations

• Global existence and asymptotic behavior for semilinear damped wave equations on measure spaces
• Fractional derivatives of composite functions and the Cauchy problem for the nonlinear half wave equation
• Stationary solution to the Navier-Stokes equations in the scaling invariant Besov space and its regularity

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