Quenching phenomena and reaction-diffusion systems in biology and medicine

Abstract

This thesis explores the topic of reaction-diffusion systems (RDSs) and their applications in biology, medicine, and bioengineering. It consists of nine chapters that cover various aspects of the subject. The thesis begins with a general introduction that emphasizes the essence of the subject and the specific issues explored in the research. The first chapter provides an overview of RDSs and their applications in different scientific disciplines. The second chapter focuses on the concept of "Quenching" and its applications in biology, medicine,and bioengineering. The third chapter introduces RDSs with initial conditions. The fourth chapter discusses first order quasilinear PDEs. Chapters five, six and seven delve into singular RDSs and the quenching phenomenon.The eighth chapter examines a quasilinear RDS of arbitrary order. The last chapter focuses on a specific class of first order quasilinear PDEs. The thesis presents theoretical frameworks, mathematical methods, and practical applications, contributing to advancements in RDSs.