Rothe's method for solving semi-linear differential equations with deviating arguments

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.

Keywords

• strong solution
• deviating argument
• semigroup of bounded linear operators
• semidiscretization method