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In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with critical, structural, dissipation, and absorbing power nonlinearity: utt+Δ2θu+2μ(−Δ)θut+|ut|p−1ut=0,t≥0,x∈Rn, with μ>0, θ is a positive integer,… Click to show full abstract
In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with critical, structural, dissipation, and absorbing power nonlinearity: utt+Δ2θu+2μ(−Δ)θut+|ut|p−1ut=0,t≥0,x∈Rn, with μ>0, θ is a positive integer, and p>1+4θ/n, in space dimension n∈(2θ,4θ). We use these estimates to find the self-similar asymptotic profile of the solutions, when μ≥1.
Keywords:
self similar;
equation critical;
similar asymptotic;
asymptotic profile;
evolution equation
Journal Title: Mathematical Methods in The Applied Sciences
Year Published: 2017
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Journal Title: Mathematical Methods in The Applied Sciences
Year Published: 2017
Link to full text (if available)
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recommendations!