Electronic Journal of Differential Equations, 
Vol. 2020 (2020), No. 120, pp. 1-10.

Title: Rothe's method for solving semi-linear differential equations with deviating arguments
       
Authors: Darshana Devi  (Tezpur Univ., Sonitpur, Assam, India)
         Duranta Chutia (Tezpur Univ., Sonitpur, Assam, India)
         Rajib Haloi    (Tezpur Univ., Sonitpur, Assam, India)

Abstract:
 We consider a semi-linear differential equation of parabolic type with deviating
 arguments in a Banach space with  uniformly convex dual, and  apply 
 Rothe's method to establish the existence and uniqueness of a strong solution.
 We also include an example as an application of the main result.
 
Submitted October 23, 2020. Published December 10, 2020.
Math Subject Classifications: 34G20, 34K30, 35D35, 35K58.
Key Words: Strong solution; deviating argument; semigroup of bounded linear operators;  
           semidiscretization method