Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping. II (Q1590092)
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scientific article; zbMATH DE number 1545275
| Language | Label | Description | Also known as |
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| English | Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping. II |
scientific article; zbMATH DE number 1545275 |
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Asymptotic behaviors of solutions of quasilinear hyperbolic equations with linear damping. II (English)
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5 June 2001
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The paper follows the work of \textit{K. Nishihara} [J. Differ. Equations 137, No. 2, 384-395 (1997; Zbl 0881.35076)] in treating the Cauchy problem for the quasilinear hyperbolic equation \(V_{tt}-a(V_x)_x+V_t=0.\) A similar decay property of the solution is proved under weaker assumptions on smallness of the initial data. Under additional assumptions on the nonlinear term \(a(v),\) the solution to the linearized problem is still an asymptotic profile of \(V(t,x).\)
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asymptotic profile
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a priori estimate
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smallness of the initial data
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