Abstract
We study the existence and the asymptotic behavior of global solutions of the damped wave equation [Formula: see text] where a ∈ ℝ, α >1, t > 0, x ∈ ℝn, n = 1,2,3, with initial condition (u (0), ut (0)) = (φ,ψ). For α > 2 and α > 1+2 / n, we prove the existence of mild global solutions for small initial data with low regularity and which are not in L1(ℝn). Under the additional hypothesis, (2 < α < 5, when n = 3), we prove that some of these solutions are asymptotic to the self-similar solutions of the associated semi-linear heat equation [Formula: see text] with homogeneous slowly decreasing initial data behaving like c|x|-2 / (α-1) as |x|→ ∞.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
