Blow-up of solutions for an integro-differential equation with a nonlinear source
Texas State University-San Marcos, Department of Mathematics
We study the nonlinear viscoelastic wave equation utt -Δu + ∫t0 g(t - s) Δu(s)ds = |u|pu, in a bounded domain, with the initial and Dirichlet boundary conditions. By modifying the method in , we prove that there are solutions, under some conditions on the initial data, which blow up in finite time with nonpositive initial energy as well as positive initial energy. Estimates of the lifespan of solutions are also given.
Blow-up, Life span, Viscoelastic, Integro-differential equation
Wu, S. T. (2006). Blow-up of solutions for an integro-differential equation with a nonlinear source. <i>Electronic Journal of Differential Equations, 2006</i>(45), pp. 1-9.