We study the Cauchy problem for the linear double dispersion equation utt-Δutt+Δ2u-Δu-Δut=0,t≥0,x∈Rnand we derive long time decay estimates for the solution in Lp spaces and in real Hardy spaces. We employ the obtained results to study the equation with nonlinearity Δ f(u) and nonsmooth f.
D'Abbicco, M., De Luca, A. (2020). Decay estimates for the double dispersion equation with initial data in real Hardy spaces. JOURNAL OF PSEUDO-DIFFERENTIAL OPERATORS AND APPLICATIONS, 11(1), 363-386 [10.1007/s11868-019-00287-1].
Decay estimates for the double dispersion equation with initial data in real Hardy spaces
De Luca A.
2020
Abstract
We study the Cauchy problem for the linear double dispersion equation utt-Δutt+Δ2u-Δu-Δut=0,t≥0,x∈Rnand we derive long time decay estimates for the solution in Lp spaces and in real Hardy spaces. We employ the obtained results to study the equation with nonlinearity Δ f(u) and nonsmooth f.
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