Evolution Equations and Applications

In this book, we present the fundamental theory of abstract Evolution Equations by using the semigroup approach. More precisely, first we review the basic notions of Functional Analysis and Differential Analysis, secondly we study the theory of semigroups of bounded linear operators, and thirdly we consider Linear Evolution Equations and moreover we give existence results for Semilinear Evolution Equations of the form: du/dt= Au + f(t; u); t 0 ; u(0) = u0 where A is a linear operator that is the infinitesimal generator of a C0-semigroup of bounded linear operators on a Banach space and f satisfies certain Lipschitz, and Linear growth conditions. As applications we show the existence of solutions to some Homogeneous Heat Equations, classical Wave equations, nonlinear Heat Equation, and to some nonlinear Wave equation.

Autorentext
After graduating in 2009 with a Bachelor of Science Degree in Mathematicsand Computer Science from the University of Buea, Cameroon.Patrice Ndambomve went further and obtained in December 2011 a Master of Science Degree in Mathematics at The African University of Science and Technology, Abuja-Nigeria; where he is currently continuing with his PhD.