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New decay estimates for linear damped wave equations and its application to nonlinear problem
Author(s) -
Ikehata Ryo
Publication year - 2004
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.476
Subject(s) - mathematics , initial value problem , exponent , wave equation , damped wave , cauchy problem , mathematical analysis , nonlinear system , half line , exponential decay , mathematical physics , physics , quantum mechanics , boundary value problem , philosophy , linguistics
We present new decay estimates of solutions for the mixed problem of the equation v tt − v xx + v t =0, which has the weighted initial data [ v 0 , v 1 ]∈( H 1 0 (0,∞) ∩ L 1, γ (0,∞)) × (L 2 (0,∞)∩ L 1, γ (0,∞)) (for definition of L 1, γ (0,∞), see below) satisfying γ∈[0,1]. Similar decay estimates are also derived to the Cauchy problem in ℝ N for u tt −Δ u + u t =0 with the weighted initial data. Finally, these decay estimates can be applied to the one dimensional critical exponent problem for a semilinear damped wave equation on the half line. Copyright © 2004 John Wiley & Sons, Ltd.
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