Hyperbolic Partial Differential Equations

Hyperbolic Partial Differential Equations

Populations, Reactors, Tides and Waves: Theory and Applications

1st Edition - January 1, 1983

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  • Editor: Matthew Witten
  • eBook ISBN: 9781483155630

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Description

Hyperbolic Partial Differential Equations, Volume 1: Population, Reactors, Tides and Waves: Theory and Applications covers three general areas of hyperbolic partial differential equation applications. These areas include problems related to the McKendrick/Von Foerster population equations, other hyperbolic form equations, and the numerical solution. This text is composed of 15 chapters and begins with surveys of age specific population interactions, populations models of diffusion, nonlinear age dependent population growth with harvesting, local and global stability for the nonlinear renewal equation in the Von Foerster model, and nonlinear age-dependent population dynamics. The next chapters deal with various applications of hyperbolic partial differential equations to such areas as age-structured fish populations, density dependent growth in a cell colony, boll-weevil-cotton crop modeling, age dependent predation and cannibalism, parasite populations, growth of microorganisms, and stochastic perturbations in the Von Foerster model. These topics are followed by discussions of bifurcation of time periodic solutions of the McKendrick equation; the periodic solution of nonlinear hyperbolic problems; and semigroup theory as applied to nonlinear age dependent population dynamics. Other chapters explore the stability of biochemical reaction tanks, an ADI model for the Laplace tidal equations, the Carleman equation, the nonequilibrium behavior of solids that transport heat by second sound, and the nonlinear hyperbolic partial differential equations and dynamic programming. The final chapters highlight two explicitly numerical applications: a predictor-convex corrector method and the Galerkin approximation in hyperbolic partial differential equations. This book will prove useful to practicing engineers, population researchers, physicists, and mathematicians.

Table of Contents


  • Foreword

    Editor's Remarks. Hyperbolic Partial Differential Equations: A Few Opening Comments

    On the Qualitative Behavior of Populations with Age-Specific Interactions

    Simple Population Models with Diffusion

    Nonlinear Age-Dependent Population Growth Under Harvesting

    Local and Global Stability for the Solutions of a Nonlinear Renewal Equation

    Some Considerations on the Mathematical Approach to Nonlinear Age Dependent Population Dynamics

    Population Models with Globally Age-Dependent Dynamics: On Computing the Steady State

    Asymptotic Behavior of an Age-Structured Fish Population

    Density Dependent Cellular Growth in an Age Structured Colony

    A PDE Formulation and Numerical Solution for a Boll Weevil-Cotton Crop Model

    Models of Age-Dependent Predation and Cannibalism Via the McKendrick Equation

    Nonlinear Hyperbolic Partial Differential Equations for the Dynamics of Parasite Populations

    Stability Analysis of a Distributed Parameter Model for the Growth of Micro-Organisms

    Partial Differential Equations with Integral Boundary Conditions

    On Stochasticity in the Von Foerster Hyperbolic Partial Differential Equation System. Further Applications to the Modeling of an Asynchronously Dividing Cellular System

    Bifurcation of the Time Periodic Solutions of the McKendrick Equations with Applications to Population Dynamics

    Periodic Solutions of Nonlinear Hyperbolic Problems

    The Semigroup Associated with Nonlinear Age Dependent Population Dynamics

    Stability of Biochemical Reaction Tanks

    A Special ADI Model for the Laplace Tidal Equations

    Initial Boundary Value Problems for the Carleman Equation

    On the Nonequilibrium Behavior of Solids that Transport Heat by Second Sound

    Nonlinear Hyperbolic Partial Differential Equations and Dynamic Programming

    Explicit Finite Difference Predictor and Convex Corrector with Applications to Hyperbolic Partial Differential Equations

    Stable and Unstable Numerical Boundary Conditions for Galerkin Approximations to hyperbolic Systems

    Index

Product details

  • No. of pages: 253
  • Language: English
  • Copyright: © Pergamon 1983
  • Published: January 1, 1983
  • Imprint: Pergamon
  • eBook ISBN: 9781483155630

About the Editor

Matthew Witten

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