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Ultrametric Pseudodifferential Equations and Applications


Part of Encyclopedia of Mathematics and its Applications

  • Date Published: April 2018
  • availability: Available
  • format: Hardback
  • isbn: 9781107188822

£ 106.00

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About the Authors
  • Starting from physical motivations and leading to practical applications, this book provides an interdisciplinary perspective on the cutting edge of ultrametric pseudodifferential equations. It shows the ways in which these equations link different fields including mathematics, engineering, and geophysics. In particular, the authors provide a detailed explanation of the geophysical applications of p-adic diffusion equations, useful when modeling the flows of liquids through porous rock. p-adic wavelets theory and p-adic pseudodifferential equations are also presented, along with their connections to mathematical physics, representation theory, the physics of disordered systems, probability, number theory, and p-adic dynamical systems. Material that was previously spread across many articles in journals of many different fields is brought together here, including recent work on the van der Put series technique. This book provides an excellent snapshot of the fascinating field of ultrametric pseudodifferential equations, including their emerging applications and currently unsolved problems.

    • Covers not only the mathematical underpinnings, but also the practical applications of ultrametric pseudodifferential equations
    • Discusses many fascinating interdisciplinary connections
    • Contains a chapter devoted to the application of p-adic diffusion equations to model flows of fluids (e.g. oil and water) in capillary networks in porous disordered media, particularly useful for geophysicists
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    Reviews & endorsements

    'The book demonstrates a wealth of interesting recently emerging subjects within a relatively small volume. It will be useful both for specialists and students studying non-Archimedean analysis and its applications.' Anatoly N. Kochubei, Mathematical Reviews

    '[As a whole] … the book o ffers … extremely rich material, providing a complete view on the recent [research] in p-adic analysis.' Luigi Rodino, zbMATH

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    Product details

    • Date Published: April 2018
    • format: Hardback
    • isbn: 9781107188822
    • length: 250 pages
    • dimensions: 241 x 160 x 17 mm
    • weight: 0.51kg
    • contains: 5 b/w illus.
    • availability: Available
  • Table of Contents

    1. p-adic analysis: essential ideas and results
    2. Ultrametric geometry: cluster networks and buildings
    3. p-adic wavelets
    4. Ultrametricity in the theory of complex systems
    5. Some applications of wavelets and integral operators
    6. p-adic and ultrametric models in geophysics
    7. Recent development of the theory of p-adic dynamical systems
    8. Parabolic-type equations, Markov processes, and models of complex hierarchic systems
    9. Stochastic heat equation driven by Gaussian noise
    10. Sobolev-type spaces and pseudodifferential operators
    11. Non-archimedean white noise, pseudodifferential stochastic equations, and massive Euclidean fields
    12. Heat traces and spectral zeta functions for p-adic laplacians

  • Authors

    Andrei Yu. Khrennikov, Linnéuniversitetet, Sweden
    Andrei Y. Khrennikov is Professor of Mathematics at Linnaeus University, Sweden and Director of the multidisciplinary research group International Center for Mathematical Modeling (ICMM). His research interests include the foundations of quantum physics and quantum information, the foundations of probability (in particular, studies on negative probabilities), cognitive modeling, dynamical systems, p-adic and ultrametric models in psychology, physics, and geology. He is the author of 20 monographs and around 400 papers in mathematics, physics, biology, cognitive science, economics, and finance.

    Sergei V. Kozyrev, Steklov Institute of Mathematics, Moscow
    Sergei V. Kozyrev is a Leading Scientific Researcher in the Department of Mathematical Physics at the Steklov Mathematical Institute, Moscow. His research interests include ultrametric analysis and applications in physics and biology, stochastic limit of quantum dynamics and quantum dissipative phenomena, and mathematical models in biology.

    W. A. Zúñiga-Galindo, Centro de Investigación y de Estudios Avanzados del Instituto Politécnico Nacional, Mexico
    W. A. Zúñiga Galindo is a Research Professor at the Center for Research and Advanced Studies of the National Polytechnic Institute, Mexico. He is a regular member of the Colombian Academy of Exact, Physical and Natural Sciences, and of the Mexican Academy of Sciences. He is also a member of the National System of Researchers of Mexico, National Researcher Level III. His work revolves around analysis, arithmetic and geometry over non-Archimedean fields (mainly p-adic fields) and their connections with mathematical physics and applications. He has published around 50 research articles and two books.

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