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Full Description
This book provides the latest scientific advances presented at the 9ECM for mathematical modeling of the biological process of chemotaxis. The wide range of techniques presented includes seven contributions from various countries, approaches exploring different properties and numerical approaches. Taxis is an important biological process that takes place in embryonic development, cancer invasion and tumor angiogenesis, among others. In fact, it is present in everything that induces movement in living organisms. More specifically, in chemotaxis, movement is induced by a chemical agent. Mathematical models of chemotaxis, since the pioneering work of Keller and Segel, attempt to reproduce this biological process. In addition to the advantages that mathematical models can have for optimizing resources and improving treatments associated with living organisms, their study from a theoretical and numerical perspective raises a mathematical challenge. The target audience of this book is any researcher interested in the mathematical analysis of biological phenomena associated with any type of taxis and modeled with PDEs.
Contents
Chapter 1. On a linear DG approximation of chemotaxis models with damping gradient nonlinearities.- Chapter 2. Boundedness in a nonlinear chemotaxis-consumption model with
gradient terms.- Chapter 3. A short note on concentration phenomena for chemotaxis systems with local sensing.- Chapter 4. On the Cauchy problem of a chemotaxis system with indirect signal production.- Chapter 5. On traveling waves of generalized chemotaxis models of Keller-Segel type inspired in Doebner-Goldin theory.- Chapter 6. A predator-prey system with diffusion and chemotaxis.- Chapter 7. Mathematical aspects of parabolic-elliptic chemotactic systems with flux limitation.
