Solution of a Variational inequality for charge transport DNA model with vibrational and rotational coupling motion (#1483)

Authors

Cortez Gutierrez, Milton Milciades

Cortez Gutierrez, Hernan Oscar

Abstract

This paper is concerned with the solution of a variational inequality for charge transport DNA model with vibrational and rotational coupling motion. For that we use the theory of semigroup according to [9] to rewrite in vector form the system obtained from the dynamics of the Peyrard-Bishop model for vibrational motion of DNA dynamics, which has been extended and analysed by [6], that is, Ut =AU +F(U) U(0) = U0 (1) This system given by (2) stand for an initial value problem, which we show that, under suitable assumptions of the operator A and on the nonlinearity F the system supports a single global weak solution satisfying the given initial condition, for that one, we consider the Sobolev spaces which will solve the Cauchy problem. The ideas of Elena D´ıaz [4] have really been followed, who considers the Peyrard-Bishop-Holstein model, which introduces a description of polaronic effects for the transport of electrical charge in DNA. Consequently, a Schr¨odringer equation is added for electrical transport, whose indicator is the amplitude probability for an electric charge located in the nth nucleotide. Likewise, in the vibrational part, the Peyrard-Bishop model has been maintained in its continuous form, which has as its starting point the discrete form in the reference of [6].