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This book presents a focused and systematic study of chemotaxis and haptotaxis systems and their derivative models, core topics in modern biomathematics. Chemotaxis type cross diffusion equations arise naturally in modeling directed cell movement, tumor invasion, and other biological processes, yet their dynamics often involve complex nonlinearities and blow up phenomena. Over recent years, our team has carried out extensive research on the dynamical analysis and optimal control of such models. This monograph brings together these results in a unified framework, offering a clear exposition of analytical techniques-especially energy estimates-that are frequently used in this field.
The book is intended to support graduate students and young researchers entering biomathematics, providing both theoretical foundations and practical methods for studying advanced chemotaxis related PDE systems and their optimal control problems.
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