On sharp decay estimates of solutions for mildly degenerate dissipative wave equations of Kirchhoff type |
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Authors: | Kosuke Ono |
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Institution: | Department of Mathematical Sciences, The University of Tokushima, 1‐1 Minamijosanjima‐cho, Tokushima 770‐8502, Japan |
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Abstract: | We consider the initial data boundary value problem for the degenerate dissipative wave equations of Kirchhoff type ρu′′ + ∥A1/2u∥2γAu+ 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. |
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Keywords: | dissipative wave equation degenerate Kirchhoff type decay estimates |
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