Electron. J. Diff. Equ., Vol. 2010(2010), No. 01, pp. 1-20.

Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval

Andrei V. Faminskii, Nikolai A. Larkin

This paper studies nonhomogeneous initial-boundary value problems for quasilinear one-dimensional odd-order equations posed on a bounded interval. For reasonable initial and boundary conditions we prove existence and uniqueness of global weak and regular solutions. Also we show the exponential decay of the obtained solution with zero boundary conditions and right-hand side, and small initial data.

Submitted October 2, 2009. Published January 5, 2010.
Math Subject Classifications: 35M20, 35Q72
Key Words: Nonlinear boundary value problems; odd-order differential equations; existence and uniqueness.

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Andrei V. Faminskii
Department of Mathematics, Peoples Friendship University of Russia
Miklukho-Maklai str. 6, Moscow, 117198, Russia
email: andrei_faminskii@mail.ru
Nikolai A. Larkin
Departamento de Matemática, Universidade Estadual de Maringá
Av. Colombo 5790: Agencia UEM, 87020-900, Maringá, PR, Brazil
email: nlarkine@uem.br

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