Electron. J. Diff. Eqns., Vol. 2008(2008), No. 138, pp. 1-10.

Unique solvability of initial boundary-value problems for hyperbolic systems in cylinders whose base is a cusp domain

Nguyen Manh Hung, Vu Trong Luong

Abstract:
We study initial boundary-value problems for hyperbolic systems of divergence form of arbitrary order in cylinders whose base is a cusp domain. Our main results are to prove the existence, uniqueness and the smoothness with respect to time variable of generalized solutions of these problems by using the method which we will denote as "approximating boundary method".

Submitted May 8, 2008. Published October 14, 2008.
Math Subject Classifications: 35D05, 35D10, 35L55, 35M10.
Key Words: Initial boundary-value problems; hyperbolic systems; Cusp domain; approximating boundary method; generalized solution; existence; uniqueness; smoothness.

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Nguyen Manh Hung
Department of Mathematics, Hanoi University of Education
Hanoi, Vietnam
email: hungnmmath@hnue.edu.vn
Vu Trong Luong
Department of Mathematics
Taybac University, Sonla, Vietnam
email: vutrongluong@gmail.com

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