Electron. J. Diff. Equ.,
Vol. 2011 (2011), No. 05, pp. 1-8.
A generalization of Osgood's test and a comparison criterion for
integral equations with noise
Marcos J. Ceballos-Lira, Jorge E. Macias-Diaz, Jose Villa
Abstract:
In this article, we prove a generalization of Osgood's test
for the explosion of the solutions of initial-value problems.
We also establish a comparison criterion for the solution of
integral equations with noise, and provide estimations of
the time of explosion of problems arising in the investigation
of crack failures where the noise is the absolute value of the
Brownian motion.
Submitted December 7, 2010. Published January 12, 2011.
Math Subject Classifications: 45G10, 45R05, 92F05, 74R10, 74R15.
Key Words: Osgood's test; comparison criterion; time of explosion;
integral equations with noise; crack failure.
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Marcos Josias Ceballos-Lira
División Académica de Ciencias Básicas
Universidad Juárez Autónoma de Tabasco
Km. 1 Carretera Cunduacán-Jalpa de Méndez
Cunduacán, Tab. 86690, Mexico
email: marjocel_81@hotmail.com
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Jorge Eduardo Macías-Díaz
Departamento de Matemáticas y Física
Universidad Autónoma de Aguascalientes
Avenida Universidad 940, Ciudad Universitaria
Aguascalientes, Ags. 20131, Mexico
email: jemacias@correo.uaa.mx
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José Villa Morales
Departamento de Matemáticas y Física
Universidad Autónoma de Aguascalientes
Avenida Universidad 940, Ciudad Universitaria
Aguascalientes, Ags. 20131, Mexico
email: jvilla@correo.uaa.mx
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