In this paper, we find the critical exponent of global small data solutions for a damped plate equation with power nonlinearity utt-δutt+δ2u+ut=|u|p,t≥0,x∈R2,and for a system of two weakly coupled damped plate equations. We show how assuming small data in the energy space H2×H1 and in L1 is sufficient to compensate the regularity-loss type decay effect created by the rotational inertia term -δutt.
The critical exponent for the dissipative plate equation with power nonlinearity
D'ABBICCO, MARCELLO
2017-01-01
Abstract
In this paper, we find the critical exponent of global small data solutions for a damped plate equation with power nonlinearity utt-δutt+δ2u+ut=|u|p,t≥0,x∈R2,and for a system of two weakly coupled damped plate equations. We show how assuming small data in the energy space H2×H1 and in L1 is sufficient to compensate the regularity-loss type decay effect created by the rotational inertia term -δutt.File in questo prodotto:
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