Some results on the global solvability for structurally damped models with a special nonlinearity

  • P. T. Duong

Abstract

The main purpose of this paper is to prove the global (in time) existence of solution for the semilinear Cauchy problem utt+(Δ)σu+(Δ)δut=|ut|p,u(0,x)=u0(x),ut(0,x)=u1(x). The parameter δ(0,σ] describes the structural damping in the model varying from the exterior damping δ=0 up to the visco-elastic type damping δ=σ. We will obtain the admissible sets of the parameter p for the global solvability of this semilinear Cauchy problem with arbitrary small initial data u0, u1 in the hyperbolic-like case δ(σ2,σ), and in the exceptional case δ=0.
Published
25.09.2018
How to Cite
Duong, P. T. “Some Results on the Global Solvability for Structurally Damped Models With a special nonlinearity”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 70, no. 9, Sept. 2018, pp. 1211-3, https://umj.imath.kiev.ua/index.php/umj/article/view/1629.
Section
Research articles