A Study on Semi-Linear delay evolution equations with Non-Linear constraints

Abstract

This thesis deals with semi linear delay evolution equations with no linear constraints. to find an integral solution to this problem, semi linear delay evolution equations with no linear constraints is converted into the abstract functional differential equation with non-densely defined generators and solved as an inhomogeneous Cauchy problem. since non-densely defined generators are sued, we can use integrated semigroup approach to solve this problem. Age structured proliferating cell population with inherited cycle length including delay terms is modelled as a semi linear delay evolution equation with nonlinear constraints and obtained an integral solution for this model by using the above method.