TY - JOUR
T1 - Global solutions for initial-boundary value problem of quasilinear wave equations
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
UR - http://www.scopus.com/inward/record.url?scp=43049084334&partnerID=8YFLogxK
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 -