


Paper's Title:
A Nonhomogeneous Subdiffusion Heat Equation
Author(s):
JoelArturo RodriguezCeballos, AnaMagnolia Marin, RubenDario Ortiz
Instituto Tecnológico de Morelia,
Morelia, Michoacan,
Mexico
Email: joel@ifm.umich.mx
Universidad de Cartagena,
Campus San Pablo,
Cartagena de Indias, Bolivar,
Colombia
Email: amarinr@unicartagena.edu.co
Email: joel@ifm.umich.mx
Abstract:
In this paper we consider a nonhomogeneous subdiffusion heat equation of fractional order with Dirichlet boundary conditions.
Paper's Title:
Trapping of Water Waves By Underwater Ridges
Author(s):
^{1}A. M. Marin, ^{ 1}R. D. Ortiz and ^{2}J. A. RodriguezCeballos.
^{1}Facultad de Ciencias Exactas y Naturales
Universidad de Cartagena
Sede Piedra de Bolivar, Avenida del Consulado
Cartagena de Indias, Bolivar,
Colombia.
^{2}Instituto Tecnológico de
Morelia Facultad de Ciencias Fisico Matematicas
Universidad Michoacana
Tecnológico
1500, Col. Lomas de Santiaguito Edificio Be ,
Ciudad Universitaria,
58120 Morelia, Michoacan,
Mexico.
amarinr@unicartagena.edu.co,
ortizo@unicartagena.edu.co.
URL: www.unicartagena.edu.co.
Abstract:
As is wellknown, underwater ridges and
submerged horizontal cylinders can serve as waveguides for surface water waves.
For large values of the wavenumber in the direction of the ridge, there is only
one trapped wave (this was proved in Bonnet & Joly (1993, SIAM J. Appl. Math.
53, pp 15071550)).
We construct the asymptotics of these trapped waves and their frequencies at
high frequency by means of reducing the initial problem to a pair of boundary
integral equations and then by applying the method of Zhevandrov & Merzon (2003,
AMS Transl. (2) 208, pp 235284), in order to solve
them.
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