Blow up of Solutions for a System of Nonlinear Higher-order Kirchhoff-type Equations
نویسنده
چکیده
In this work, we consider the initial boundary value problem for the Kirchhoff-type equations with damping and source terms utt +M (∫ Ω ∣∣∣(−△)m2 u∣∣∣2 dx) (−△) u+ |ut| ut = f1 (u, v) , vtt +M (∫ Ω ∣∣∣(−△)m2 v∣∣∣2 dx) (−△) v + |vt| vt = f2 (u, v) in a bounded domain. We prove the blow up of the solution with positive initial energy by using the technique of [26] with a modification in the energy functional due to the different nature of problems. This improves earlier results in the literature [3, 9, 13, 21].
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