Hyperbolic–parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation |
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Authors: | Taeko Yamazaki |
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Affiliation: | Department of Mathematics, Faculty of Science and Technology, Tokyo University of Science, Noda, Chiba 278‐8510, Japan |
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Abstract: | We consider a hyperbolic–parabolic singular perturbation problem for a quasilinear hyperbolic equation of Kirchhoff type with dissipation weak in time. The purpose of this paper is to give time‐decay convergence estimates of the difference between the solutions of the hyperbolic equation above and those of the corresponding parabolic equation, together with the unique existence of the global solutions of the hyperbolic equation above. Copyright © 2009 John Wiley & Sons, Ltd. |
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Keywords: | singular perturbation Kirchhoff equation quasilinear hyperbolic equation weak dissipation nonlinear PDE of hyperbolic type |
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