Nguyen Thanh Long, Le Xuan Truong
We study the initial-boundary value problem for the nonlinear wave equation
where , , are given constants and are given functions. The unknown function and the unknown boundary value satisfy the linear integral equation
where are given functions satisfying some properties stated in the next section. This paper consists of two main sections. First, we prove the existence and uniqueness for the solutions in a suitable function space. Then, for the case , we find the asymptotic expansion in of the solutions, up to order .
Submitted October 27, 2006. Published March 20, 2007.
Math Subject Classifications: 35L20, 35L70.
Key Words: Nonlinear wave equation; linear integral equation; existence and uniqueness; asymptotic expansion.
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| Nguyen Thanh Long |
Department of Mathematics
Hochiminh City National University
227 Nguyen Van Cu, Q5, HoChiMinh City, Vietnam
email: firstname.lastname@example.org, email@example.com
| Le Xuan Truong |
Department of Mathematics, Faculty of General Science
University of Technical Education in HoChiMinh City
01 Vo Van Ngan Str., Thu Duc Dist., HoChiMinh City, Vietnam
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