Author | Fife, Paul C. author |
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Title | Mathematical Aspects of Reacting and Diffusing Systems [electronic resource] / by Paul C. Fife |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1979 |
Connect to | http://dx.doi.org/10.1007/978-3-642-93111-6 |
Descript | IV, 185 p. online resource |
Preface and General Introduction -- 1. Modeling Considerations -- 1.1 Basic hypotheses -- 1.2 Redistribution processes -- 1.3 Boundaries and interfaces -- 1.4 Reactions with migration -- 1.5 The reaction mechanism -- 1.6 Positivity of the density -- 1.7 Homogeneous systems -- 1.8 Modeling the rate functions -- 1.9 Colony models -- 1.10 Simplifying the model by means of asymptotics -- 2. Fisherโs Nonlinear Diffusion Equation and Selection-Migration Models -- 2.1 Historical overview -- 2.2 Assumptions for the present model -- 2.3 Reduction to a simpler model -- 2.4 Comments on the comparison of models -- 2.5 The question of formal approximation -- 2.6 The case of a discontinuous carrying capacity -- 2.7 Discussion -- 3. Formulation of Mathematical Problems -- 3.1 The standard problems -- 3.2 Asymptotic states -- 3.3 Existence questions -- 4. The Scalar Case -- 4.1 Comparison methods -- 4.2 Derivative estimates -- 4.3 Stability and instability of stationary solutions -- 4.4 Traveling waves -- 4.5 Global stability of traveling waves -- 4.6 More on Lyapunov methods -- 4.7 Further results in the bistable case -- 4.8 Stationary solutions for x-dependent source function -- 5. Systems: Comparison Techniques -- 5.1 Basic comparison theorems -- 5.2 An example from ecology -- 6. Systems: Linear Stability Techniques -- 6.1 Stability considerations for nonconstant stationary solutions and traveling waves -- 6.2 Pattern stability for a class of model systems -- 7. Systems: Bifurcation Techniques -- 7.1 Small amplitude stationary solutions -- 7.2 Small amplitude wave trains -- 7.3 Bibliographical discussion -- 8. Systems: Singular Perturbation and Scaling Techniques -- 8.1 Fast wave trains -- 8.2 Sharp fronts (review) -- 8.3 Slowly varying waves (review) -- 8.4 Partitioning (review) -- 8.5 Transient asymptotics -- 9. References to Other Topics -- 9.1 Reaction-diffusion systems modeling nerve signal propagation -- 9.2 Miscellaneous -- References