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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)
Galerkin method
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##### References:
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