A Parameter Property of Classical Solutions of Cauchy Problems
Abstract & Applied Analysis
cauchy problem, semigroups (algebra), parabolic differential equations, mathematical models, integral operators
Analysis | Applied Mathematics | Mathematics
This work is concerned with the abstract Cauchy problems that depend on parameters. The goal is to study continuity in the parameters of the classical solutions of the Cauchy problems. The situation considered in this work is when the operator of the Cauchy problem is not densely defined. By applying integrated semigroup theory and the results on continuity in the parameters ofC0-semigroup and integrated semigroup, we obtain the results on the existence and continuity in parameters of the classical solutions of the Cauchy problems. The application of the obtained abstract results in a parabolic partial differential equation is discussed in the last section of the paper.
He, Min (2014). A Parameter Property of Classical Solutions of Cauchy Problems. Abstract & Applied Analysis . doi: 10.1155/2014/363089 Retrieved from https://digitalcommons.kent.edu/mathpubs/8