In this paper, we study the critical exponent for the beam equation with nonlinear memory, i.e., utt+Δ2u = F(t, u) , where (Formula presented.). 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).
The beam equation with nonlinear memory
D'ABBICCO, MARCELLO;LUCENTE, SANDRA
2016-01-01
Abstract
In this paper, we study the critical exponent for the beam equation with nonlinear memory, i.e., utt+Δ2u = F(t, u) , where (Formula presented.). 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).File in questo prodotto:
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