TY - JOUR
T1 - Globally Lipschitz continuous solutions to a class of quasilinear wave equations
AU - Chang, Yuan
AU - Hong, John M.
AU - Hsu, Cheng Hsiung
N1 - Funding Information:
* Corresponding author. E-mail addresses: [email protected] (Y. Chang), [email protected] (J.M. Hong), [email protected] (C.-H. Hsu). 1 The authors were supported in part by the National Science Council of Taiwan and Center for Theoretical Sciences, Mathematical Division, NCU.
PY - 2007/5/15
Y1 - 2007/5/15
N2 - This work investigates the existence of globally Lipschitz continuous solutions to a class of Cauchy problem of quasilinear wave equations. Applying Lax's method and generalized Glimm's method, we construct the approximate solutions of the corresponding perturbed Riemann problem and establish the global existence for the derivatives of solutions. Then, the existence of global Lipschitz continuous solutions can be carried out by showing the weak convergence of residuals for the source term of equation.
AB - This work investigates the existence of globally Lipschitz continuous solutions to a class of Cauchy problem of quasilinear wave equations. Applying Lax's method and generalized Glimm's method, we construct the approximate solutions of the corresponding perturbed Riemann problem and establish the global existence for the derivatives of solutions. Then, the existence of global Lipschitz continuous solutions can be carried out by showing the weak convergence of residuals for the source term of equation.
KW - Cauchy problem
KW - Generalized Glimm's method
KW - Hyperbolic systems of balance laws
KW - Lax's method
KW - Perturbed Riemann problem
KW - Quasilinear wave equations
UR - http://www.scopus.com/inward/record.url?scp=34247101812&partnerID=8YFLogxK
U2 - 10.1016/j.jde.2007.02.006
DO - 10.1016/j.jde.2007.02.006
M3 - 期刊論文
AN - SCOPUS:34247101812
SN - 0022-0396
VL - 236
SP - 504
EP - 531
JO - Journal of Differential Equations
JF - Journal of Differential Equations
IS - 2
ER -