Weak, Strong and Global Solutions for DNA Model with Memory

Objective: To determine solutions of hyperbolic partial differential equations with memory using operator techniques with the corresponding estimates. The hyperbolic model associated with the Peyrard-Bishop model of DNA with memory is especially analyzed. Method: Using Gronwall inequalities and operator theory, solutions to partial differential equations are obtained after reduction to an equivalent one. Results and Discussion: The existence of three types of weak, strong and global solutions for the hyperbolic model associated with the Peyrard-Bishop model of DNA with memory has been demonstrated. Implications of the research: Apply in the first university years the application of MATLAB and Python to partial differential equations in all university careers and specialties as part of the management of the tools of Information and Communication Technology (TIC). Originality/Value: This paper also provides an alternative approach to Analysis of DNA vibration amplitudes with past-dependent memory.