Blow-up of solutions to systems of nonlinear wave equations with supercritical sources Article

Guo, Y, Rammaha, MA. (2013). Blow-up of solutions to systems of nonlinear wave equations with supercritical sources . APPLICABLE ANALYSIS, 92(6), 1101-1115. 10.1080/00036811.2011.649734

cited authors

  • Guo, Y; Rammaha, MA

authors

abstract

  • In this article, we focus on the life span of solutions to the following system of nonlinear wave equations: in a bounded domain Ω ⊂ ℝnwith Robin and Dirichlét boundary conditions on u and v, respectively. The nonlinearities f1(u, v) and f2(u, v) represent strong sources of supercritical order, while g1(ut) and g2(vt) represent interior damping. The nonlinear boundary condition on u, namely ∂νu + u + g(ut) = h(u) on Γ, also features h(u), a boundary source, and g(ut), a boundary damping. Under some restrictions on the parameters, we prove that every weak solution to system above blows up in finite time, provided the initial energy is negative. © 2013 Copyright Taylor and Francis Group, LLC.

publication date

  • June 1, 2013

published in

Digital Object Identifier (DOI)

start page

  • 1101

end page

  • 1115

volume

  • 92

issue

  • 6