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The global solution and blow-up phenomena to a modified Novikov equation

Shaoyong Lai*, Haibo Yan and Nan Li

Author Affiliations

Department of Applied Mathematics, Southwestern University of Finance and Economics, Chengdu, 610074, China

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Boundary Value Problems 2014, 2014:16  doi:10.1186/1687-2770-2014-16

Published: 15 January 2014

Abstract

A modified Novikov equation with symmetric coefficients is investigated. Provided that the initial value <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M1','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M1">View MathML</a> (<a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M2','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M2">View MathML</a>), <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M3','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M3">View MathML</a> does not change sign and the solution u itself belongs to <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M4','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M4">View MathML</a>, the existence and uniqueness of the global strong solutions to the equation are established in the space <a onClick="popup('http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M5','MathML',630,470);return false;" target="_blank" href="http://www.boundaryvalueproblems.com/content/2014/1/16/mathml/M5">View MathML</a>. A blow-up result to the development of singularities in finite time for the equation is acquired.

MSC: 35G25, 35L05.

Keywords:
global existence; strong solutions; blow-up result