Global solutions for initial-boundary value problem of quasilinear wave equations

John M. Hong; Cheng Hsiung Hsu; Ying Chin Su

doi:10.1016/j.jde.2008.02.013

Global solutions for initial-boundary value problem of quasilinear wave equations

John M. Hong, Cheng Hsiung Hsu, Ying Chin Su

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

This work investigates the existence of globally Lipschitz continuous solutions to a class of initial-boundary value problem of quasilinear wave equations. Applying the Lax's method and generalized Glimm's method, we construct the approximate solutions of initial-boundary Riemann problem near the boundary layer and perturbed Riemann problem away from the boundary layer. By showing the weak convergence of residuals for the approximate solutions, we establish the global existence for the derivatives of solutions and obtain the existence of global Lipschitz continuous solutions of the problem.

Original language	English
Pages (from-to)	223-248
Number of pages	26
Journal	Journal of Differential Equations
Volume	245
Issue number	1
DOIs	https://doi.org/10.1016/j.jde.2008.02.013
State	Published - 1 Jul 2008

Keywords

Generalized Glimm's method
Hyperbolic systems of balance laws
Initial and boundary Riemann problem
Lax's method
Perturbed Riemann problem
Quasilinear wave equations

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10.1016/j.jde.2008.02.013

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title = "Global solutions for initial-boundary value problem of quasilinear wave equations",

abstract = "This work investigates the existence of globally Lipschitz continuous solutions to a class of initial-boundary value problem of quasilinear wave equations. Applying the Lax's method and generalized Glimm's method, we construct the approximate solutions of initial-boundary Riemann problem near the boundary layer and perturbed Riemann problem away from the boundary layer. By showing the weak convergence of residuals for the approximate solutions, we establish the global existence for the derivatives of solutions and obtain the existence of global Lipschitz continuous solutions of the problem.",

keywords = "Generalized Glimm's method, Hyperbolic systems of balance laws, Initial and boundary Riemann problem, Lax's method, Perturbed Riemann problem, Quasilinear wave equations",

author = "Hong, {John M.} and Hsu, {Cheng Hsiung} and Su, {Ying Chin}",

note = "Funding Information: * Corresponding author. E-mail addresses: [email protected] (J.M. Hong), [email protected] (C.-H. Hsu), [email protected] (Y.-C. Su). 1 Research supported in part by the National Science Council of Taiwan. 2 Research supported in part by the National Science Council of Taiwan and the National Center for Theoretical Sciences of Taiwan.",

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AU - Hong, John M.

AU - Hsu, Cheng Hsiung

AU - Su, Ying Chin

N1 - Funding Information: * Corresponding author. E-mail addresses: [email protected] (J.M. Hong), [email protected] (C.-H. Hsu), [email protected] (Y.-C. Su). 1 Research supported in part by the National Science Council of Taiwan. 2 Research supported in part by the National Science Council of Taiwan and the National Center for Theoretical Sciences of Taiwan.

PY - 2008/7/1

Y1 - 2008/7/1

N2 - This work investigates the existence of globally Lipschitz continuous solutions to a class of initial-boundary value problem of quasilinear wave equations. Applying the Lax's method and generalized Glimm's method, we construct the approximate solutions of initial-boundary Riemann problem near the boundary layer and perturbed Riemann problem away from the boundary layer. By showing the weak convergence of residuals for the approximate solutions, we establish the global existence for the derivatives of solutions and obtain the existence of global Lipschitz continuous solutions of the problem.

AB - This work investigates the existence of globally Lipschitz continuous solutions to a class of initial-boundary value problem of quasilinear wave equations. Applying the Lax's method and generalized Glimm's method, we construct the approximate solutions of initial-boundary Riemann problem near the boundary layer and perturbed Riemann problem away from the boundary layer. By showing the weak convergence of residuals for the approximate solutions, we establish the global existence for the derivatives of solutions and obtain the existence of global Lipschitz continuous solutions of the problem.

KW - Generalized Glimm's method

KW - Hyperbolic systems of balance laws

KW - Initial and boundary Riemann problem

KW - Lax's method

KW - Perturbed Riemann problem

KW - Quasilinear wave equations

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U2 - 10.1016/j.jde.2008.02.013

DO - 10.1016/j.jde.2008.02.013

M3 - 期刊論文

AN - SCOPUS:43049084334

SN - 0022-0396

VL - 245

SP - 223

EP - 248

JO - Journal of Differential Equations

JF - Journal of Differential Equations

IS - 1

ER -

Global solutions for initial-boundary value problem of quasilinear wave equations

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