# Initial value problems and first boundary problems for a class of quasilinear wave equations

Initial value problems and first boundary problems for a class of quasilinear wave equations The initial value problems and the first boundary problems for the quasilinear wave equation $$u_{tt} - \left[ {a_0 + na_1 \left( {u_x } \right)^{n - 1} } \right]u_{xx} - a_2 u_{xxtt} = 0$$ are considered, wherea 0,a 2 > 0 are constants,a 1 is an arbitrary real number,n is a natural number. The existence and uniqueness of the classical solutions for the initial value problems and the first boundary problems of the equation (1) are proved by the Galerkin method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

# Initial value problems and first boundary problems for a class of quasilinear wave equations

, Volume 9 (4) – Jul 13, 2005
13 pages

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Publisher
Springer Journals
Copyright © 1993 by Science Press, Beijing, China and Allerton Press, Inc. New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02005918
Publisher site
See Article on Publisher Site

### Abstract

The initial value problems and the first boundary problems for the quasilinear wave equation $$u_{tt} - \left[ {a_0 + na_1 \left( {u_x } \right)^{n - 1} } \right]u_{xx} - a_2 u_{xxtt} = 0$$ are considered, wherea 0,a 2 > 0 are constants,a 1 is an arbitrary real number,n is a natural number. The existence and uniqueness of the classical solutions for the initial value problems and the first boundary problems of the equation (1) are proved by the Galerkin method.

### Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 13, 2005

### References

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