Mathematical Analysis and Approximation of PDE-Chemotaxis Models

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Inbunden, Engelska, 2026

AvCristian Morales-Rodrigo,María Ángeles Rodríguez-Bellido,Antonio Suárez

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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.

Produktinformation

Utgivningsdatum2026-04-29
Mått155 x 235 x undefined mm
FormatInbunden
SpråkEngelska
SerieSEMA SIMAI Springer Series
Antal sidor165
FörlagSpringer Nature Switzerland AG
ISBN9783032147882

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Beräkning och matematisk analys inom Naturvetenskap och teknik

Cristian Morales Rodrigo is an associate professor of Mathematical Analysis at the Department of Differential Equations and Numerical Analysis at the Universidad de Sevilla, Spain and the Institute of Mathematics of the Universidad de Sevilla (IMUS). His research focuses on the analysis of PDEs applied to biology, more precisely on population and chemotaxis models. María Ángeles Rodríguez Bellido is an associate professor of Mathematical Analysis at the Department of Differential Equations and Numerical Analysis at the Universidad de Sevilla, Spain and the Institute of Mathematics of the Universidad de Sevilla (IMUS). Her research focuses on Partial Differential Equations (PDEs), including the mathematical and numerical analysis of PDEs systems applied to other sciences: Oseen and Navier-Stokes equations, primitive ocean equations, liquid crystal models, quasi-Newtonian fluids, Boussinesq equations, and chemotaxis models. She has completed research stays at the Universities of Clermont-Ferrand, Savoy and Pau (France), UNICAMP-SP and Federal University of Pernambuco (Brazil), La Serena, Bío-Bío and Tarapacá (Chile), UIS-Bucaramanga (Colombia), and the Czech Academy of Sciences in Prague (Czech Republic). Antonio Suárez Fernández is a full professor at the Department of Differential Equations and Numerical Analysis and the Institute of Mathematics of the Universidad de Sevilla (IMUS). His research interests include the theoretical analysis of partial differential equations (PDEs) applied to other sciences. In particular, he has studied PDEs related to populations dynamics with special emphasis on problems with diffusion and non-local terms.

Chapter 1. On a linear DG approximation of chemotaxis models with damping gradient nonlinearities.- Chapter 2. Boundedness in a nonlinear chemotaxis-consumption model withgradient 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.