Blow‐up for the b‐family of equations |
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| Authors: | Fernando Cortez |
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| Institution: | Escuela Politécnica Nacional, Departamento de Matemática, Facultad de Ciencias, Quito, Ecuador |
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| Abstract: | In this paper, we consider the b‐family of equations on the torus u t ?u t x x +(b + 1)u u x =b u x u x x +u u x x x , which for appropriate values of b reduces to well‐known models, such as the Camassa–Holm equation or the Degasperis–Procesi equation. We establish a local‐in‐space blow‐up criterion. Copyright © 2016 John Wiley & Sons, Ltd. |
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| Keywords: | Degasperis ‐ Procesi Camassa ‐ Holm b ‐ family of equations blow‐up local criterion |
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