Global existence of solutions of Cauchy problem for generalized system of nonlinear evolution equations arising from DNA

Abstract

In this paper, we prove that the Cauchy problem for the generalized system of the nonlinear evolution equations arising from DNA utt−σuxx−uxxtt=f(v)xx, vtt−vxxtt=g(v)xx has a unique global generalized solutions in C2([0,∞);Hs×Hs), a unique global classical solution, and the sufficient conditions of blow up of solution in finite time are given. We also prove that the Cauchy problem has a unique global generalized solution in C2([0,∞);Wm,p∩L∞×Wm,p∩L∞) and a unique global classical solution.