an:00549494
Zbl 0822.35094
Chen, Guowang; Yang, Zhijian; Zhao, Zhancai
Initial value problems and first boundary problems for a class of quasilinear wave equations
EN
Acta Math. Appl. Sin., Engl. Ser. 9, No. 4, 289-301 (1993).
00017497
1993
j
35L70 35A05
Galerkin method
Summary: The initial value problems and the first boundary problems for the quasilinear wave equation
\[
u_{tt}- [a_ 0+ na_ 1 (u_ x)^{n-1} ]u_{xx}- a_ 2 u_{xxtt} =0
\]
are considered, where \(a_ 0, a_ 2>0\) are constants, \(a_ 1\) is an arbitrary real number, \(n\) is a natural number. The existence and uniqueness of classical solutions are proved by the Galerkin method.