Geodesic
Blow-up of solutions for an integro-differential equation with a nonlinear source
Electronic journal of differential equations, Tome 2006 (2006)
We study the nonlinear viscoelastic wave equation

$ u_{tt}-\Delta u+\int_0^t g(t-s)\Delta u(s)ds=|u|^p u, $

in a bounded domain, with the initial and Dirichlet boundary conditions. By modifying the method in [15], 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.
Classification : 35L05, 35L15, 35L70, 37B25
Keywords: blow-up, life span, viscoelastic, integro-differential equation 
@article{EJDE_2006__2006__a21,
     author = {Wu,  Shun-Tang},
     title = {Blow-up of solutions for an integro-differential equation with a nonlinear source},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1112.35345},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a21/}
}
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Wu,  Shun-Tang. Blow-up of solutions for an integro-differential equation with a nonlinear source. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a21/