In this paper we determine Lp−Lq estimates, 1≤p≤q≤∞, for the solution to the Cauchy problem for the damped wave equation utt−Δu+(−Δ)θ2ut=0,t≥0,x∈ℝnu(0,x)=0,ut(0,x)=u1(x); in the case of very strong damping, θ>2.
$$L^p-L^q$$ Estimates for Very Strongly Damped Wave Equations
D'Abbicco, Marcello
;Lagioia, Antonio
2025-01-01
Abstract
In this paper we determine Lp−Lq estimates, 1≤p≤q≤∞, for the solution to the Cauchy problem for the damped wave equation utt−Δu+(−Δ)θ2ut=0,t≥0,x∈ℝnu(0,x)=0,ut(0,x)=u1(x); in the case of very strong damping, θ>2.File in questo prodotto:
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