×

zbMATH — the first resource for mathematics

Initial value problems and first boundary problems for a class of quasilinear wave equations. (English) Zbl 0822.35094
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.

MSC:
35L70 Second-order nonlinear hyperbolic equations
35A05 General existence and uniqueness theorems (PDE) (MSC2000)
Keywords:
Galerkin method
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zhang Shanyuan, Zhuang Wei, Strain Solitary Waves in the Nonlinear Elastic Rods,Acta Mechanica Sinica,20 (1988), 58–66 (in Chinese).
[2] Zhou Yulin and Fu Hongyuan, Nonlinear Hyperbolic Systems of Higher Order of Generalized Sine-Gorden Type,Acta Mathematicae Sinica,26 (1983), 234–249 (in Chinese). · Zbl 0538.35055
[3] Gagliardo, E., Ulterlori Proprieta di alcune classl di funzioni inpiu variablli.Ric. Mat.,8 (1959), 24–51. · Zbl 0199.44701
[4] Nirenberg, L., On Eillptic Partial Differential Equations (Lecture II),Ann. Sc. Norm. Super. Pisa, S.3:13 (1952), 115–162.
[5] Yoslda, K., Functional Analysis, Springer-Verlag, Berlin, 1978
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.