Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping Article

Guo, Y, Rammaha, MA, Sakuntasathien, S et al. (2014). Hadamard well-posedness for a hyperbolic equation of viscoelasticity with supercritical sources and damping . JOURNAL OF DIFFERENTIAL EQUATIONS, 257(10), 3778-3812. 10.1016/j.jde.2014.07.009

cited authors

  • Guo, Y; Rammaha, MA; Sakuntasathien, S; Titi, ES; Toundykov, D

authors

abstract

  • Presented here is a study of a viscoelastic wave equation with supercritical source and damping terms. We employ the theory of monotone operators and nonlinear semigroups, combined with energy methods to establish the existence of a unique local weak solution. In addition, it is shown that the solution depends continuously on the initial data and is global provided the damping dominates the source in an appropriate sense.

publication date

  • November 15, 2014

published in

Digital Object Identifier (DOI)

start page

  • 3778

end page

  • 3812

volume

  • 257

issue

  • 10