rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Parabolic Equations in Biology
    sub title: Growth, reaction, movement and diffusion
  name:
    name part: Perthame, Benoît.
    role:
      role term: creator
    role:
      role term: author.
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: gw
    date issued: 2015
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XII, 199 p. 39 illus., 13 illus. in color. online resource.
  abstract: This book presents several fundamental questions in mathematical biology such as Turing instability, pattern formation, reaction-diffusion systems, invasion waves and Fokker-Planck equations. These are classical modeling tools for mathematical biology with applications to ecology and population dynamics, the neurosciences, enzymatic reactions, chemotaxis, invasion waves etc. The book presents these aspects from a mathematical perspective, with the aim of identifying those qualitative properties of the models that are relevant for biological applications. To do so, it uncovers the mechanisms at work behind Turing instability, pattern formation and invasion waves. This involves several mathematical tools, such as stability and instability analysis, blow-up in finite time, asymptotic methods and relative entropy properties. Given the content presented, the book is well suited as a textbook for master-level coursework.
  table of contents: 1.Parabolic Equations in Biology -- 2.Relaxation, Perturbation and Entropy Methods -- 3.Weak Solutions of Parabolic Equations in whole Space -- 4.Traveling Waves -- 5.Spikes, Spots and Pulses -- 6.Blow-up and Extinction of Solutions -- 7.Linear Instability, Turing Instability and Pattern Formation -- 8.The Fokker-Planck Equation -- 9.From Jumps and Scattering to the Fokker-Planck Equation -- 10.Fast Reactions and the Stefan free Boundary Problem.
  note: by Benoît Perthame.
  subject:
    topic: Mathematics
  subject:
    topic: Applied mathematics
  subject:
    topic: Engineering mathematics
  subject:
    topic: Biomathematics
  subject:
    topic: Mathematics
  subject:
    topic: Mathematical and Computational Biology
  subject:
    topic: Applications of Mathematics
  classification: QH323.5
  classification: QH324.2-324.25
  classification: 570.285
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Lecture Notes on Mathematical Modelling in the Life Sciences
  identifier: 9783319195001
  identifier: http://dx.doi.org/10.1007/978-3-319-19500-1
  record info:
    record creation date: 150909
    record change date: 20151103131424.0
    record identifier: 978-3-319-19500-1