Ukrainian Mathematical Journal

, Volume 70, Issue 9, pp 1395–1418 | Cite as

Some Results on the Global Solvability for Structurally Damped Models with Special Nonlinearity

  • P. T. Duong
The main purpose of the paper is to prove the global (in time) existence of solution for the semilinear Cauchy problem
$$ {u}_{tt}+{\left(-\Delta \right)}^{\sigma }u+{\left(-\Delta \right)}^{\delta }{u}_t={\left|{u}_t\right|}^p,\kern0.5em u\left(0,x\right)={u}_0(x),\kern0.5em {u}_t\left(0,x\right)={u}_1(x). $$

The parameter δ ∈ (0, σ] describes the structural damping in the model varying from the exterior damping δ = 0 to the viscoelastic type damping δ = σ. We determine 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 \( \delta \in \left(\frac{\sigma }{2},\sigma \right) \) and in the exceptional case δ = 0.


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • P. T. Duong
    • 1
  1. 1.Hanoi National University of EducationHanoiVietnam

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