Abstract
In this paper, we study the critical exponent for the beam equation with nonlinear memory, i.e., \({u_{tt}+\Delta^2u = F(t, u)}\), where
For suitable f and p, we prove the existence of local-in-time solutions and small data global solutions to the Cauchy problem, in homogeneous and nonhomogeneous Sobolev spaces. In some cases, we prove that the local solution cannot be extended to a global one. We also consider the limit case of power nonlinearity, i.e., \({F = N(u)}\).
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