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Self‐similar asymptotic profile of the solution to a nonlinear evolution equation with critical dissipation
Author(s) -
D'Abbicco M.,
Ebert M. R.,
Lucente S.
Publication year - 2017
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.4469
Subject(s) - mathematics , dissipation , dimension (graph theory) , nonlinear system , integer (computer science) , evolution equation , space (punctuation) , mathematical analysis , power (physics) , mathematical physics , pure mathematics , physics , thermodynamics , quantum mechanics , linguistics , philosophy , computer science , programming language
In this paper, we obtain optimal decay estimates for the solutions to an evolution equation with critical, structural, dissipation, and absorbing power nonlinearity:u t t +Δ2 θ u + 2 μ ( − Δ ) θ u t + | u t | p − 1u t = 0 , t ≥ 0 , x ∈ R n ,with μ >0, θ is a positive integer, and p >1+4 θ / n , in space dimension n ∈(2 θ ,4 θ ). We use these estimates to find the self‐similar asymptotic profile of the solutions, when μ ≥1.