We study the Cauchy problem for the semilinear structural damped wave equation with source term utt-Δu+μ(-Δ)σut=f(u), u(0,x)=u0(x),ut(0,x)=u1(x),with σ∈(0,1] in space dimensionn≥2 and with a positive constant μ. We are interested in the influence of σ on the critical exponent pcrit in|f(u)|≈|u|p. This critical exponent is the threshold between global existence in time of small data solutions and blow-up behavior for some suitable range of p. Our results are optimal for σ=1/2. Copyright © 2013 John Wiley & Sons, Ltd.
Semilinear structural damped waves
D'ABBICCO, MARCELLO;
2014-01-01
Abstract
We study the Cauchy problem for the semilinear structural damped wave equation with source term utt-Δu+μ(-Δ)σut=f(u), u(0,x)=u0(x),ut(0,x)=u1(x),with σ∈(0,1] in space dimensionn≥2 and with a positive constant μ. We are interested in the influence of σ on the critical exponent pcrit in|f(u)|≈|u|p. This critical exponent is the threshold between global existence in time of small data solutions and blow-up behavior for some suitable range of p. Our results are optimal for σ=1/2. Copyright © 2013 John Wiley & Sons, Ltd.File in questo prodotto:
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