Abstract
For or one spatial variable, a new kind of coupled system for nonlinear wave equations of Emden-Fowler type is considered with boundary value and initial values. Under certain conditions on the initial data and the exponent rho, we show that the viscoelastic terms lead our problem to be dissipative and that the global solutions cannot exist in L-2 beyond the given finite time i.e.,
integral(r2)(r1) (vertical bar u(1)vertical bar(2) + vertical bar u(2)vertical bar(2) dx -> +infinity as t -> T*,
Where
In T* = 2/rho +1 (Sigma(2)(i=1) integral(r2)(r1) vertical bar u(i0)vertical bar(2) dx) (Sigma(2)(i=1) integral(r2)(r1) (2u(i0)u(i1) - vertical bar u(i0)vertical bar(2)) dx)(-1).