• Bulletin of the Korean Mathematical Society
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• v.38 no.3
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• pp.505-516
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• 2001

We show the existence and uniqueness of solutions for the Cauchy problem for nonlinear evolution equations with the strong damping: ${\upsilon}"(t)-M(｜{\nablauu}(t)｜^2){\triangle}u(t)-{\delta}{\triangle}u'(t)=f(t)$. As an application, a Kirchhoff model with viscosity is given.