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The Keller-Segel model for chemotaxis is a prototype of nonlocal
systems describing concentration phenomena in physics and biology.
While the two-dimensional theory is by now quite complete, the
questions of global-in-time solvability and blowup characterization
are largely open in higher dimensions. In this book, global-in-time
solutions are constructed under (nearly) optimal assumptions on
initial data and rigorous blowup criteria are derived.
This book presents original problems from graduate courses in pure
and applied mathematics and even small research topics, significant
theorems and information on recent results. It is helpful for
specialists working in differential equations.
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