Electron. J. Diff. Eqns., Vol. 2008(2008), No. 35, pp. 1-11.

Existence and smoothness of solutions to second initial boundary value problems for Schrodinger systems in cylinders with non-smooth bases

Nguyen Manh Hung, Nguyen Thi Kim Son

Abstract:
In this paper, we consider the second initial boundary value problem for strongly general Schrodinger systems in both the finite and the infinite cylinders $Q_T, 0<T\leq +\infty$, with non-smooth base $\Omega$. Some results on the existence, uniqueness and smoothness with respect to time variable of generalized solution of this problem are given.

Submitted December 5, 2007. Published March 12, 2008.
Math Subject Classifications: 35D05, 35D10, 35G99.
Key Words: Second initial boundary value problem; Schrodinger systems; 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
Nguyen Thi Kim Son
Department of Mathematics, Hanoi University of Education
Hanoi, Vietnam
email: mt02_02@yahoo.com

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