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book: Cross-Diffusion Systems
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Cross-Diffusion Systems

Dynamics, Coexistence and Persistence
  • Dung Le
Language: English
Published/Copyright: 2025
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De Gruyter Series in Nonlinear Analysis and Applications

About this book

The introduction of cross diffusivity opens many questions in the theory of reactiondiffusion systems. This book will be the first to investigate such problems presenting new findings for researchers interested in studying parabolic and elliptic systems where classical methods are not applicable. In addition, The Gagliardo-Nirenberg inequality involving BMO norms is improved and new techniques are covered that will be of interest. This book also provides many open problems suitable for interested Ph.D students.

• Introduces dynamical systems for applications in biology and ecology

• Covers the main components in cross-diffusion systems and coexistence of geometry-affected steady states

• Discussed global existence and persistence of evolution processes

Author / Editor information

Dung Le, University of Texas, San Antonio, USA.

Topics

  • Publicly Available

    Frontmatter

    I
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    Dedication

    V
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    Contents

    VII
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    1 Introduction

    1
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    2 Preliminaries

    11
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    3 Existence results for cross-diffusion systems

    44
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    4 Scalar techniques and diagonalization

    71
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    5 Existence of solutions to general elliptic systems

    121
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    6 Existence of solutions to elliptic systems of two equations

    137
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    7 Persistence in the dynamics of evolution processes

    182
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    8 Coexistence of a class of cross-diffusion systems of m equations via index theories

    213
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    9 Global and local Gagliardo–Nirenberg inequalities with a BMO term and fractional Laplacians

    240
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    Bibliography

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    Index

    279
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Publishing information
Pages and Images/Illustrations in book
eBook published on:
September 8, 2025
eBook ISBN:
9783111615677
Hardcover published on:
September 8, 2025
Hardcover ISBN:
9783111615578
Edition:
2nd, revised and expanded edition
Pages and Images/Illustrations in book
Front matter:
10
Main content:
282
https://doi.org/10.1515/9783111615677
eBook ISBN: 9783111615677
Hardcover ISBN: 9783111615578
Keywords for this book
Strongly coupled; Elliptic/parabolic system; BMO (Bounded Mean Oscillation); Regularity; Steady states
Audience(s) for this book
Researchers, graduate students in theoretical mathematics biology, and applied mathematicians.
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