Manuel Milla Miranda, Aldo T. Louredo, Luiz A. Medeiros
Abstract:
In this article we study the existence and uniqueness of local solutions
for the initial-boundary value problem for the Kirchhoff equation
where
is a bounded domain of
with its boundary
constiting of two disjoint parts
and
;
is a real number;
is the exterior unit normal vector at
and
are real functions defined in
and
,
respectively.
Our result is obtained using the Galerkin method with a special basis,
the Tartar argument, the compactness approach, and a Fixed-Point method.
Submitted January 24, 2017. Published March 21, 2017.
Math Subject Classifications: 35L15, 35L20, 35K55, 35L60, 35L70.
Key Words: Kirchhoff equation; nonlinear boundary condition;
existence of solutions.
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Manuel Milla Miranda Universidade Estadual da Paraíba DM, PB, Brazil email: milla@im.ufrj.br | |
Aldo T. Louredo Universidade Estadual da Paraíba DM, PB, Brazil email: aldolouredo@gmail.com Phone: +55 (83) 3315-3340 | |
Luiz A. Medeiros Universidade Federal do Rio de Janeiro IM, RJ, Brazil email: luizadauto@gmail.com |
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