Self-similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation
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DOI: 10.1002/mma.4469
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… read more here.
Keywords: self similar; equation critical; similar asymptotic; asymptotic profile ... See more keywords
Asymptotic profile of solutions for strongly damped Klein‐Gordon equations
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DOI: 10.1002/mma.5508
Abstract: We consider the Cauchy problem in the whole space for strongly damped Klein-Gordon equations. We derive asymptotic profles of solutions with weighted initial data by a simple method introduced by R. Ikehata. The obtained results… read more here.
Keywords: profile solutions; strongly damped; klein gordon; asymptotic profile ... See more keywords
Asymptotic profile of solutions to the linearized double dispersion equation on the half space $\mathbb{R}^{n}_{+}$
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DOI: 10.3934/eect.2017032
Abstract: In this paper, we investigate the initial boundary value problem for the linearized double dispersion equation on the half space \begin{document}$\mathbb{R}^{n}_{+}$\end{document} . We convert the initial boundary value problem into the initial value problem by… read more here.
Keywords: profile solutions; equation; value problem; asymptotic profile ... See more keywords