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Applicable Analysis
An International Journal
Volume 29, 1988 - Issue 1-2
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Original Articles

Hyperbolic-parabolic singular perturbations for scalar nonlinearities

B.F. Esham Jr. Department of Mathematical Sciences, Virginia Commonwealth University
&
B.F. Weinacht Department of Mathematical Sciences, University of Delaware
Pages 19-44 | Received 22 Oct 1987, Published online: 02 May 2007

Citations (15)

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Y.S. Lee. (1991) Singular perturbation of a nonlinear time-dependent problem in hilbert space. Applicable Analysis 40:2-3, pages 189-209.
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Articles from other publishers (14)

R. Altmann & C. Zimmer. (2022) Singular perturbation results for linear partial differential–algebraic equations of hyperbolic type. Journal of Mathematical Analysis and Applications 511:2, pages 126095.
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Marina Ghisi & Massimo Gobbino. (2011) Hyperbolic–parabolic singular perturbation for nondegenerate Kirchhoff equations with critical weak dissipation. Mathematische Annalen 354:3, pages 1079-1102.
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Marina Ghisi & Massimo Gobbino. (2012) Hyperbolic–parabolic singular perturbation for mildly degenerate Kirchhoff equations: Decay-error estimates. Journal of Differential Equations 252:11, pages 6099-6132.
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Marina Ghisi & Massimo Gobbino. (2010) Mildly degenerate Kirchhoff equations with weak dissipation: Global existence and time decay. Journal of Differential Equations 248:2, pages 381-402.
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Taeko Yamazaki. (2009) Hyperbolic-parabolic singular perturbation for quasilinear equations of Kirchhoff type with weak dissipation. Mathematical Methods in the Applied Sciences 32:15, pages 1893-1918.
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Hiromichi Hashimoto & Taeko Yamazaki. (2007) Hyperbolic–parabolic singular perturbation for quasilinear equations of Kirchhoff type. Journal of Differential Equations 237:2, pages 491-525.
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Marina Ghisi & Massimo Gobbino. (2006) Global–in–time Uniform Convergence for Linear Hyperbolic–Parabolic Singular Perturbations. Acta Mathematica Sinica, English Series 22:4, pages 1161-1170.
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Ralph Chill & Alain Haraux. (2004) An Optimal Estimate for the Time Singular Limit of an Abstract Wave Equation. Funkcialaj Ekvacioj 47:2, pages 277-290.
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Mohan K. Kadalbajoo & Kailash C. Patidar. (2003) Singularly perturbed problems in partial differential equations: a survey. Applied Mathematics and Computation 134:2-3, pages 371-429.
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Massimo Gobbino. (2001) Singular perturbation hyperbolic–parabolic for degenerate nonlinear equations of Kirchhoff type. Nonlinear Analysis: Theory, Methods & Applications 44:3, pages 361-374.
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Tokio Matsuyama. (1999) Quasilinear hyperbolic–hyperbolic singular perturbations with nonmonotone nonlinearity. Nonlinear Analysis: Theory, Methods & Applications 35:5, pages 589-607.
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Benjamin F. EshamJr.Jr. & Elizabeth Greenwell Yanik. (1991) Galerkin methods for a singularly perturbed hyperbolic problem with nonlocal nonlinearity. Computers & Mathematics with Applications 22:2, pages 1-22.
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Benjamin F. EshamJr.Jr.. (2005) A hyperbolic singular perturbation of Burgers' equation. Mathematical Methods in the Applied Sciences 12:1, pages 77-90.
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Benjamin F. Esham, Jr.Richard J. Weinacht. (1989) Hyperbolic-Parabolic Singular Perturbations for Quasilinear Equations. SIAM Journal on Mathematical Analysis 20:6, pages 1344-1365.
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