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Exponential stability and blow up for a problem with Balakrishnan-Taylor damping

Tatar N.-E., Zaraï A.

Demonstratio Mathematica

2011

Vol. 44, nr 1

67-90

This work is devoted to the study of a nonlinear viscoelastic Kirchhoff equation with Balakrishnan-Taylor damping. We show that the weak dissipation producedby the memory term is strong enough to stabilize solutions exponentially. Also, we show that a nonlinear source of polynomial type is able to force solutions to blow up in finite time even in presence of a stronger damping.