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CONVERGENCE RATES TO ASYMPTOTIC PROFILE FOR SOLUTIONS OF QUASILINEAR HYPERBOLIC EQUATIONS WITH LINEAR DAMPING.
- Source :
-
Journal of Hyperbolic Differential Equations . Mar2011, Vol. 8 Issue 1, p115-129. 15p. - Publication Year :
- 2011
-
Abstract
- This paper is concerned with the asymptotic behavior of the solution of quasilinear hyperbolic equations with linear damping. The main novelty lies in the following observation: If we suitably choose the initial data of the corresponding parabolic equation, then the solution Ψ = Ψ(x, t) of the parabolic equation served as the new asymptotic profile satisfies |(V-Ψ, (V-Ψ)x, (V-Ψ)t)(t)|L∞ = O(1)(t-2, t-5/2, t-3). The convergence rates of the new profile Ψ are better than that obtained by H.-J. Zhao (2000, J. Differential Equations167, 467-494), and we need none of the additional technical assumptions (H1) and (H2) therein. Therefore, we answer an open problem posed by Nishihara (1997, J. Differential Equations133, 384-395). [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 02198916
- Volume :
- 8
- Issue :
- 1
- Database :
- Academic Search Index
- Journal :
- Journal of Hyperbolic Differential Equations
- Publication Type :
- Academic Journal
- Accession number :
- 60398415
- Full Text :
- https://doi.org/10.1142/S0219891611002342