Decay estimates of solutions for mildly degenerate Kirchhoff type dissipative wave equations in unbounded domains

Article type: Research Article

Authors: Ono, Kosuke

Affiliations: Department of Mathematical Sciences, The University of Tokushima, 1-1 Minamijosanjima-cho, Tokushima 770-8502, Japan. E-mail: ono@ias.tokushima-u.ac.jp

Abstract: We consider the Cauchy problem for mildly degenerate Kirchhoff type dissipative wave equations: ρu″+‖A1/2u(t)‖2γAu+u′=0 in RN×R+, u(x,0)=u0(x), u′(x,0)=u1(x) in RN, with ρ>0, γ≥1, and ‖A1/2u0‖>0. When either the coefficient ρ or the initial data {u0,u1} are small, we prove the existence of global solutions by using several identities for energies. Moreover, we derive lower decay estimates of the solutions, and upper decay estimates of their second order derivatives.

Keywords: Kirchhoff strings, degenerate equations, decay rates

DOI: 10.3233/ASY-141215

Journal: Asymptotic Analysis, vol. 88, no. 1-2, pp. 75-92, 2014