Chapter 1. Large time behavior of solutions to the chemotaxis-fluid -- Chapter 2. Global existence in Keller--Segel-- Navier--Stokes system involving tensor-valued sensitivity -- Chapter 3. Large time behavior of solutions to chemotaxis--haptotaxis models -- Chapter 4. Large time behavior of Keller--Segel--(Navier)--Stokes system modeling coral fertilization -- Chapter 5. Qualitative properties to density-suppressed motility models -- Chapter 6. Large time behavior of multi-taxis cross-diffusion system.

Open Access

This open access book deals with a rich variety of taxis-type cross-diffusive equations. Particularly, it intends to show the key role played by quasi-energy inequality in the derivation of some necessary a priori estimates. This book addresses applied mathematics and all researchers interested in mathematical development of reaction-diffusion theory and its application and can be a basis for a graduate course in applied mathematics.