Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
840027 | Nonlinear Analysis: Theory, Methods & Applications | 2014 | 16 Pages |
Abstract
In this paper we study the influence of a nonlinear memory F(t,u)=∫0t(t−s)−γ∣u(s,x)∣pds,γ∈(0,1), on the global existence of small data solutions to utt−△u+ut=F(t,u),u(0,x)=u0(x),ut(0,x)=u1(x), in space dimension 1≤n≤51≤n≤5. We prove the global existence for p>p̄(n,γ), where p̄(n,γ) is the critical exponent , i.e. no global weak solution exists for 1
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Authors
M. D’Abbicco,