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On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type
Author(s) -
Ono Kosuke
Publication year - 2011
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.1443
Subject(s) - dissipative system , degenerate energy levels , mathematics , type (biology) , mathematical analysis , wave equation , initial value problem , small data , boundary value problem , mathematical physics , physics , quantum mechanics , ecology , biology , computer science , data mining
We consider the initial data boundary value problem for the degenerate dissipative wave equations of Kirchhoff type ρu′′ + ∥ A 1/2 u ∥ 2γ Au + u ′ = 0. When either the coefficient ρ or the initial data are appropriately small at least, we show the global existence theorem by using suitable identities together with the energy. Moreover, under the same assumption for ρ and the initial data, we derive the sharp decay estimates of the solutions and their second derivatives. Copyright © 2011 John Wiley & Sons, Ltd.